This is a Phase Ib, open-label, dose-escalation study to determine the Maximal tolerated dose (MTD) and the recommended Phase 2 dose (RP2D) for the combination of afuresertib and paclitaxel in subjects with recurrent HER2-negative gastric cancer, and further assess safety and preliminary efficacy of combination at the RP2D. Afuresertib had showed synergistic activity when combined with paclitaxel in vitro and in vivo models of gastric cancer. Dose escalation will continue until the MTD is established. The dose schedule is once daily (QD) dosing for afuresertib and intravenous (IV) infusion for paclitaxel Dose escalation in Part 1 will follow the 3 + 3 cohort design. A sequential approach will be conducted to explore the optimal paclitaxel regimen (weekly or 3weekly schedule) when combined with afuresertib. The dose escalation will be started from Cohort A (afuresertib combined with weekly paclitaxel regimen at 80 milligram (mg)/meter (m)^2 day1, 8,15, every 4 weeks (q4w). The starting dose in Cohort A will be 125 mg afuresertib QD. Once its MTD is identified, and then the study will move to dosing Cohort B (afuresertib combined with 3 weekly paclitaxel regimen at 175 mg/m^2 day1, every 3 week (q3w). The starting daily dose of Cohort B will be 25 mg less than the MTD dose from Cohort A for afuresertib. If it is tolerated, then the dose escalation schedule will be followed in Cohort B until the MTD in this Cohort is reached. If the starting dose is not tolerated, then dose de-escalation will be explored until the MTD in this Cohort is reached. Once two dimensions of the MTD are achieved, then the optimal regimen for paclitaxel and MTD for afuresertib combined with paclitaxel based on the toxicity profile will be identified. The combination regimen at the RP2D selected following Part I will be further investigated in its efficacy and safety in the Part II Expansion Cohort. Once a combination dose regimen for Part 2 has been determined, at least 20 and up to 40 subjects will be enrolled at the dose regimen selected following Part I. Overall response rate (ORR) will be evaluated using a Green-Dahlberg design. The design consists with one interim analysis. If less than 3 responses are observed in the initial 20 subjects, enrollment will be terminated due to futility; otherwise, the study will continue to meet the planned sample size of 40 subjects.

Inclusion Criteria:

• Provided signed written informed consent
• Male or female >=18 years of age with a diagnosis of Performance Status score of 0 or 1 according to the Eastern Cooperative Oncology at the time of signing the informed consent
• Able to swallow and retain orally administered study treatment
• Women of childbearing potential must have a negative serum pregnancy test within 7 days prior to the first dose of study treatment and agree to use effective contraception during the study. Men with a female partner of childbearing potential must have either had a prior vasectomy or agree to use effective contraception (Condom [during non-vaginal intercourse with any partner - male or female] OR Double-barrier method: condom and occlusive cap (diaphragm or cervical/vault caps) plus spermicidal agent (foam/gel/film/cream/suppository) [during sexual intercourse with a female]. Abstinence, defined as sexual inactivity consistent with the preferred and usual lifestyle of the subject. Periodic abstinence (e.g. calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception.
• Adequate organ system functions at screening as Hematologic system (Absolute neutrophil count >=1.5 x 10^9/Litre (L), Hemoglobin >=9.0 gram (g)/deci (d)L, Platelets >=100 x 10^9/microL without transfusion in the past 7 days, prothrombin time/ international normalized ratio (PT/INR) and partial thromboplastin time (PTT) <=1.5 x Upper limit of normal [ULN]), Hepatic system (Total bilirubin <=1.0x ULN, Aspartate aminotransferase (AST) and Alanine aminotransferase (ALT) <=2.5x ULN), Metabolic system (Fasting Serum Glucose < 126 milli (m)g/dL [7 millimol/L], Hemoglobin A1C<=8%) and Renal system (Serum creatinine <= ULN, 24-hour urine creatinine clearance >=60 mL/minute [min])
• Histologically confirmed from the stomach or gastroeosophageal (GE) junction cancer with documented HER2-negative (defined as immunohistochemistry (IHC) 0-1+ or IHC2+ with a negative fluorescent in situ hybridization (FISH) test assessed by local or designated central lab) in primary or metastatic tumor tissue.
• Metastatic or locally advanced, unresectable disease.
• Subjects must have received first-line platinum/fluoropyrimidine doublet regimen for advanced gastric cancer and now exhibit progressive disease (PD), and must have recovered from any treatment-related toxicity. Note: prior XELOX, XP, FOLFOX, or SP (S-1+cisplatin)) treatment could be eligible, but prior-taxane are ineligible. Note: if patient is refractory or disease progression within 6 months of adjuvant treatment, then his previous treatment would be considered as first line treatment rather than adjuvant treatment, and then this patient could be enrolled into this study if other inclusion/exclusion criterion meets.
• Subjects shall have at least one measurable disease (i.e., present with at least one measurable lesion) by RECIST version1.1

Exclusion Criteria:

• History of another malignancy. Exception: Subjects who have been disease-free for 3 years, or subjects with a history of completely resected non-melanoma skin cancer or successfully treated in situ carcinoma are eligible.
• Prior PI3K-AKT- mammalian target of rapamycin (mTOR) pathway targeted therapy will not be eligible. (Note: prior vaccine and immunotherapy is allowed but must end at least 8 weeks prior to study treatment).
• Unresolved toxicity (Grade <=1) from prior chemotherapy with the exception of alopecia or anemia (Hemoglobin >9 g/dL).
• Subjects with uncontrolled brain metastases or spinal cord compression.
• Current use of warfarin for therapeutic anticoagulation (Note: low molecular weight heparin is permitted).
• Presence of an active gastrointestinal disease (not including gastric cancer), or other condition known to interfere significantly with the absorption, distribution, metabolism, or excretion of drugs. Prior gastrectomy is allowed.
• History of myocardial infarction, acute coronary syndromes (including unstable angina), coronary angioplasty, or stenting or bypass grafting within six months of Screening.
• Pregnant or lactating female.
• Any serious and/or unstable pre-existing medical, psychiatric disorder or other conditions that could interfere with subject's safety, obtaining informed consent or compliance to the study procedures.
• Any prohibited medication(s) as Co-administration of afuresertib and medications which are a sensitive substrate of CYP3A4, OATP1B1 and BCRP with a low therapeutic index will be prohibited. Coadministration of afuresertib and medications which are a sensitive substrate of CYP2C8 with a low therapeutic index will be used with caution.
• History of Type 1 diabetes
• Any major surgery within the last four weeks.
• QTcF interval >=470 milliseconds (msec)s.
• known immediate or delayed hypersensitivity reaction or idiosyncratic reaction to drugs similar or related to afuresertib and taxanes.
• Any contraindications (as identified by the investigator) to the doses of paclitaxel defined in the protocol.
• Any history of reduction in standard of care paclitaxel dose for peripheral neuropathy.
• Known Human Immunodeficiency Virus (HIV) infection or active hepatitis B or C. (Note: active Hepatitis B virus (HBV) infection is defined as ALT/AST is above or equal to normal range or HBV deoxyribonucleic acid (DNA) >=2×10^3-4 international unit (IU)/mL; active Hepatitis C virus (HCV) infection is defined as HCV ribonucleic acid (RNA)+ and ALT/AST is above normal range). Antiviral therapy should be initiated before study treatment, and maintain during study treatment in patients with inactive HBV infection. Prophylaxis against HBV reactivation is recommended in accordance with established guidelines: the Asian-Pacific census statement on HBV in 2012 and Taiwan health insurance guidance in 2013.