This is an open-label, single arm study to evaluate the safety and tolerability of treatment with CT053 CAR-BCMA T in patients with relapsed and/or refractory multiple myeloma.

The study is composed of two stages, Phase I stage is for dose escalation and recommendation of phase 2 dose, and Phase II stage is to Detailed Description: verify the efficacy and safety of the dose proposed.

Inclusion Criteria:

1. Patients and legally acceptable representative must have voluntarily signed ICF and willing to complete the study procedure, after fully understanding of the study.

2. Age ≥ 18 years and ≤ 75 years, male or female

3. The patients have received at least 3 prior lines for MM, (Induction therapy followed by autologous transplantation[ASCT] and maintenance therapy represents one line of therapy, those who have not been treated with ASCT should have documented rationale); For each line of therapy, the patient should have received at least one standard treatment cycle (2016 IMWG) unless the best response to the treatment line is documented as progressive diseases (PD)

4. The patients should have received treatment with at least one proteasome inhibitor AND one immunomodulatory drug, and have ever been relapsed or deteriorated after treatment with at least one regimen consisting of above-mentioned medications (combination or single use)；

5. Patient should be relapsed within 12 months after the last line of therapy, or disease progressed within 60 days after last line of therapy (IMWG criteria 2016), with documented evidence.

6. The patients should have measurable disease based on at least one of the following parameters：

   • Serum M-protein ≥ 10 g/L;
   • Urine M-protein ≥ 200 mg/24 hrs;
   • For those whose Serum or Urine M- protein dose not meed the measurable criteria but the light chain type, serum free light chain (FLC): involved FLC level ≥ 10 mg/dL (100 mg/L) provided serum FLC ratio is abnormal

7. Estimated life expectancy > 12 weeks

8. ECOG performance score 0-1；

9. Sufficient venous access for leukapheresis collection, and no other contraindications to leukapheresis

10. Patients should maintain adequate organ function

11. Women of childbearing age must undergo a serum pregnancy test with negative results before screening and lymphodepletion preconditioning with fludarabine and cyclophosphamide, and are willing to use effective and reliable method of contraception for at least 1 year after T cell infusion

12. Men who actively have intercourse with child-bearing potential women must be willing to use effective and reliable method of contraception for at least 1 year after T cell infusion

Exclusion Criteria:

1. Pregnant or lactating women；
2. Positive for any following tests: human immunodeficiency virus (HIV) antibody, Treponema Pallidum antibody, hepatitis C virus (HCV) antibody, hepatitis B virus (HBV) surface antigen (HBsAg), HBV e antigen (HBeAg), HBV e antibody, hepatitis B core antibody, HBV DNA;
3. Patients with any uncontrolled active infection including but not limited to active tuberculosis.
4. Patients with AEs from previous treatment that have not recovered to Common Terminology Criteria for Adverse Events (CTCAE) ≤ 1, excluding hair loss, neuropathy and other events that the treating physician can determine to be tolerable.
5. Patients who have ever had any CAR T cell therapy；
6. Patients who have ever had anti-BCMA therapy；
7. Patients have received allogeneic stem cell transplantation for treating multiple myeloma;
8. Patients have received autologous stem cell transplantation less than 12 weeks before leukapheresis；
9. Patients have received any anti-cancer treatment within 14 days before leukapheresis including but not limited to cytotoxic therapy, proteasome inhibitors, immunomodulatory agents, targeted therapies, epigenetic therapy or experimental drug therapy. If the field of radiation covers ≤ 5% of the bone marrow, the subjects are eligible to participate in the study regardless of the radiotherapy end date；
10. Patients have received ≥ 5 mg prednisone daily or other equivalent dose of steroids within 14 days before leukapheresis or lymphodepletion；
11. Patients have plasma cell leukemia, Waldenström macroglobulinemia, POEMS (polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy, and skin changes) syndrome or AL amyloidosis；
12. Patients have been administered live attenuated vaccine 4 weeks before leukapheresis or lymphodepletion
13. Patients allergic to component of study treatment.
14. Patients have any of the condition as following within 6 months of ICF sign-off: New York Heart Association (NYHA) stage III or IV congestive heart failure, angina pectoris, myocardial infarction, coronary artery bypass graft, stroke (excluding lacunar stroke), history of clinically significant arrhythmia including but not limited to ventricular arrhythmia, significant QT interval prolongation, uncontrolled blood pressure as defined as systolic > 160 mmHg, diastolic > 100 mmHg, uncontrolled diabetes mellitus, pulmonary thrombolism, other conditions that investigators believe that participating in this clinical trial may endanger the health of the patients
15. Patients are known to have active autoimmune diseases including but not limited to psoriasis, rheumatoid arthritis and other needs of long-term immunosuppressive therapy
16. patients are oxygen dependent as defined by the blood oxygen saturation (finger oxygen detection method) can be maintained > 95% only by oxygen inhalation before leukapheresis
17. Patients with second malignancies in addition to MM are not eligible if the second malignancy has required treatment within the past 5 years or is not in complete remission. There are two exceptions to this criterion: successfully treated cervical carcinoma in situ and non-metastatic basal cell skin carcinoma
18. Patients have central nervous system (CNS) metastases or CNS involvement (including cranial neuropathies or mass lesions and leptomeningeal disease). Patients with history of spinal cord compression from MM are eligible provided spinal cord compression has been treated with surgery or radiation at least 28 days prior to study entry
19. Patients are unable or unwilling to comply with the requirements of clinical trial
20. Patients have received major surgery 2 weeks prior to leukapheresis or 4 weeks prior to lymphodepletion and after the study treatment (excluding cataract and other local anesthesia)
21. Patients are relatives to investigator or his/her staff, or those who may have an interest in the investigator and/or his/her staff.