This study aims to evaluate the safety and tolerance of modified CD19 CAR T cells in treating refractory/relapsed B-cell malignancies. CAR-T cells will be investigated as a single agent both in relapsed/refractory B-cell acute lymphoblastic leukaemia (B-ALL) and up to 60% of patients with B-cell non-Hodgkin's lymphoma (NHL).

Inclusion Criteria:

1. Male or female aged 18-70 years;

2. Estimated survival time ≥ 12 weeks;

3. Histologically confirmed diagnosis of CD19+ B-ALL or CD19+ B-NHL(meeting one of the following conditions):

   1. Ineffectively or relapses after 2 or more remedial treatments
   2. Relapse after auto-HSCT or unsuitable for auto-HSCT;

4. At least one assessable tumor lesion;

5. ECOG performance status 0 to 2;

6. Creatinine clearance rate≥ 60 ml/min, ALT and AST ≤ 2.5 times of upper limit of normal, total bilirubin ≤ 1.5 times of upper limit of normal;

7. Male and female of reproductive potential must agree to use birth control during the study and for at least 30 days post study;

8. Patients or their legal guardians volunteer to participate in the study and sign the informed consent.

Exclusion Criteria:

1. Patients with other uncontrolled malignancies;
2. Previously treated with any CAR-T cell product or other genetically-modified T cell therapy;
3. Patients with HIV infection, hepatitis B (HBsAg positive) or hepatitis C（anti-HCV positive);
4. Patients with central nervous system involvement by lymphoma ,malignant cells in cerebrospinal fluid or history of brain metastasis;
5. Patients with atrial or ventricular involvement by B-cell malignancies;
6. Patients with tumor mass require urgent treatment, such as ileus or vascular compression;
7. Patients with severe disease or other uncontrolled diseases that were not suitable for this trial, such as coronary heart disease, angina pectoris, myocardial infarction, arrhythmia, cerebral thrombosis, cerebral hemorrhage, grade 2-3 hypertension;
8. Unstable pulmonary embolism, deep venous embolism, or other major arterial/venous thromboembolism events occurred within 30 days prior to randomization. If patients receive anticoagulant therapy, the treatment dose must be stable prior to randomization;
9. Any situations that the investigators believes were not suitable for this trial;
10. Long-term use of immunosuppressive agents after organ transplantation, except for the patients recently or currently receiving inhaled steroids;
11. Pregnant(or lactation) women;
12. Patients with severe active infections(excluding simple urinary tract infection and bacterial pharyngitis)within 30 days prior to randomization