Inclusion Criteria:

• Must have bi-dimensionally measurable, recurrent or chemotherapy - or Rituxan-refractory aggressive B-cell NHL (Diffuse large B-cell, transformed B-cell lymphoma, or Mantle cell lymphoma)
• Patient who relapse after autologous (not allogeneic) stem cell transplantation are eligible.
• Patients must have had prior Rituximab therapy, with response duration of at least 6 months to the last Rituximab-based therapy (single agent or in combination)
• No anti-lymphoma therapy within the past 3 weeks, and no radiation therapy within 2 weeks.
• Patients must not be eligible for treatment of a higher priority.
• Must have a good performance status (<3 Zubrod, >/=60 Karnofsky).
• Must have a good marrow reserve: ANC >/=1,000, Platelets >/=75,000.
• Bilirubin </= 2mg/dl, SGOT or SGPT </= x 5 normal values.
• Age > 18 (There is no information about the toxicity of Bevacizumab especially adverse effects on growth and development in pediatric patients).
• Must sign a consent form.
• Must have a life expectancy of > 12 weeks.

Exclusion Criteria:

• HIV positive
• History of serious cardiac disease such as myocardial infarction within 6 months of treatment, brady- or tachyarrhythmia, or clinically uncontrolled hypertension (blood pressure >160/110 mmHg).
• Active infection or history of opportunistic infection.
• Pregnant women or breast-feeding women.
• Women of child-bearing age who are not practicing adequate contraception.
• History of prior DVT or pulmonary embolus.
• INR > 1.5
• Serum creatinine > 2mg/dl, or clinically significant proteinuria (patients with >1+ proteinuria should have 24 hour urine collection and those with >2gm/day should be excluded).
• Evidence of bleeding diathesis or coagulopathy.
• History of other cancers within 5 years except for basal cell carcinoma of the skin.
• Radiotherapy within 14 days of Day 0.
• Current, recent (within 21 days of Day 0), or planned participation in an experimental drug study.
• Hemoglobin <9gm/dl (may be transfused or receive epoetin alfa [e.g., Epogen]to maintain or exceed this level).
• History of other disease, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that might affect the interpretation of the results of the study or render the subject at high risk from treatment complications.
• Serious, non-healing wound, ulcer, or bone fracture.
• History of CNS disease (including CNS involvement from primary cancer) or hemorrhagic or thrombotic stroke within the last 6 months.
• History of hemoptysis requiring transfusion and/or hospitalization within the last 5 years.
• Anatomic lesion that increase the risk of serious hemorrhage (e.g., invasion of a major vessel by tumor).
• Current, ongoing treatment with full-dose warfarin or its equivalent.
• Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to Day 0.
• Fine needle aspirations, indwelling catheter placement, or core biopsy within 7 days prior to Day 0.
• Anticipation of need for major surgical procedure during the course of the study.