• CD19 positive B-cell malignancies confirmed as one of the following: aggressive or indolent B-cell NHL, philadelphia chromosome-positive or -negative B-cell ALL, or B-cell CLL; patient must meet the definition of relapse/refractory before enrollment.

• ECOG (Eastern Cooperative Oncology Group) performance status 0-2, life expectancy \>3 months；

• Clinical laboratory values as specified below during the Screening period.

‣ Total bilirubin \<1.5 ULN, may be elevated up to 3 x ULN if the elevation can be reasonably ascribed to the presence of metastatic disease in the liver or in patients with documented Gilbert's Syndrome;

⁃ ALT or AST \<3ULN, may be elevated up to 5 x ULN if the elevation can be reasonably ascribed to the presence of metastatic disease in liver;

⁃ Calculated creatinine clearance \> 50 mL/min (The Cockcroft-Gault formula);

⁃ Hemoglobin ≥ 7 g/dL;

⁃ Neutrophil count \> 1,000/mm3 for B-cell NHL patient;

⁃ Platelet count \> 75,000/mm3 for B-cell NHL patient;

⁃ B-ALL patients must have peripheral blast count ≤ 30,000/ mm3 prior to first dose of CC312.

⁃ Prothrombin time-international normalized ratio (PT-INR) ≤ 1.5ULN.

• Female patients of childbearing potential or male patients with a partner of childbearing potential must use one or more contraception methods from screening and continued during study treatment until 3 months after the last dose;

• Ability to understand and willingness to provide written informed consent and to comply with scheduled visits and study procedures.