The goal of this clinical trial is to study the safety and efficacy of lenvatinib combined with single-agent taxanes therapy in patients with HER2-negative advanced gastric cancer that have failed at the standard first-line therapy.

This study is being conducted to establish safety and preliminary efficacy of Lenvatinib plus taxane drugs treatment for HER2-negative advanced gastric cancer after failure of first-line treatment.

The study will adopt the "3+3" dose escalation design. All patients received a standard dose of chemotherapy: paclitaxel 135mg/m2 every 3 weeks or docetaxel 75mg/m2 every 3 weeks. Lenvatinib is exploring four doses of 4mg, 8mg, 12mg, and 16mg, orally once a day every 3 weeks. In the first cycle, lenvatinib was administered 5 days before chemotherapy，once a day. Chemotherapy lasts up to 6 cycles, and lenvatinib continues to be administered until the disease progresses, intolerable side effects, or death.

In order to avoid the possible ineffectiveness caused by the patient being exposed to low doses, the initial dose of 4 mg was enrolled in 1 patient. If there is no obvious dose-limiting toxicity (DLT) after the first dose, the dose escalation adopts a "3+3" method from the 8mg dose: if none of the 3 subjects in the previous dose group has a DLT within 21 days, the next dose study will be carried out; if one subject in the group has DLT occurs, then 3 additional subjects should be added to the dose group; if the 3 subjects have 1 or more DLTs, the trial terminated and the previous dose was regarded as the maximum tolerated dose (MTD).

Inclusion Criteria:

1. Ability to understand and the willingness to provide written informed consent.
2. Advanced gastric cancer diagnosed by histopathological or cytological examination, no uncontrollable pleural and ascites;.
3. Age no less than 18 years.
4. Life expectancy greater than 3 months.
5. According to the RECIST (Response Evaluation Criteria in Solid Tumors) standard, there must be measurable lesions.
6. Failed at the standard first-line therapy, microsatellite stable (MSS) or no mismatch repair missing(PMMR), HER2 negative.
7. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 .
8. Adequate liver/bone marrow function.
9. Female subjects must meet the following conditions: infertility or fertility and use high-efficiency contraceptive measures.
10. Male subjects agree to use approved contraceptive methods (e.g. birth control pills, barrier device, intrauterine device, abstinence) during the study and for 3 months following the last dose of the study cell infusion. Moreover, all men are absolutely prohibited from donating sperm within 1 year after receiving the last study treatment infusion.

Exclusion Criteria:

1. Previous use of lenvatinib or chemotherapy drugs in the regimen.
2. Pregnant or breast-feeding female, or not willing to take contraception measures during study.
3. Uncontrolled brain metastasis or mental illness.
4. Suffered from other uncured malignant tumors within the past 3 years or at the same time.
5. A history of active gastrointestinal bleeding within 3 months, incomplete obstruction or complete intestinal obstruction.
6. Uncontrollable high blood pressure are not suitable for enroll into the study.
7. Other uncontrolled diseases may cause abnormal death of the patient.
8. Untolerable liver/bone marrow function.
9. Factors that affect the administration of oral drugs (dysphagia, chronic diarrhea, complete intestinal obstruction, etc.
10. Previously allergic to the ingredients of the medicine in regimen.
11. Can't be followed up or obey protocol.
12. The investigator believes that it is not appropriate to participate in the trial.