Inclusion Criteria: - 18 years of age or older - Karnofsky Performance Status 60 or greater - Life expectancy of at least 8 weeks - Histologic diagnosis of GBM, gliosarcoma, anaplastic astrocytoma (AA), anaplastic oligodendroglioma (AO), or anaplastic mixed oligoastrocytoma (AMO) - Unequivocal progression by magnetic resonance imaging (MRI) or computed tomography (CT) scan. A scan must be performed within 14 days prior to registration and on a steroid dose that has been stable for at least 5 days. The same type of scan must be used throughout the period of protocol treatment for tumor measurement. Subjects with recurrence who undergo resection and are left without measurable or evaluable disease are eligible. - Patients must have failed prior radiation therapy and must have an interval of greater than or equal to 60 days from the completion of radiation therapy to study entry. - Patients must have recovered from the toxic effects of prior therapy. Residual toxicity from any previous treatment must be Grade 1 or less. - Sufficient time for recovery from prior therapy: 28 days from any investigational agent, 28 days from prior cytotoxic therapy, and 7 days for non-cytotoxic agents. - Patients with prior therapy that included interstitial brachytherapy or stereotactic radiosurgery must have confirmation of true progressive disease rather than radiation necrosis based upon positron emission tomography (PET), Thallium scanning, MR spectroscopy or surgical documentation of disease. - Subjects who have undergone recent resection of recurrent or progressive tumor will be eligible as long as all of the following conditions apply: a) prior to initiating therapy, 4 weeks must have elapsed since surgery b) residual disease following resection of recurrent malignant glioma is not mandated for eligibility. To assess the extent of residual disease postoperatively, a MRI or CT should be done at least 4 weeks postoperatively and within 14 days prior to registration. - Clinical laboratory tests within 14 days prior to enrollment meeting the criteria listed in the protocol - Cardiology assessment: Baseline MUGA or Echocardiogram must demonstrate LVEF 50% or greater - Electrocardiogram: 3 sequential ECGs separated by at least 5 minutes. Each individual pretreatment QTc interval must be 460 msec or less and the average of the QTc intervals must be 450 msec or less. - Patients in non-hypertensive or has well-controlled hypertension (systolic blood pressure of < 140mm Hg or diastolic pressure < 90 mm Hg). - Female subjects of childbearing potential must have a negative pregnancy test confirmed within 48 hours prior to dosing with the study drug - Subjects must be free of any clinically relevant disease (other than recurrent GBM or gliosarcoma) that would, in the Investigator's opinion, interfere with the conduct of the study or study evaluations. PHASE I Inclusion Criteria (the following modifications to the general eligibility criteria apply to Phase I patients only): - Patients may have been treated for any number of prior relapses. Relapse is defined as progression following initial therapy - Patients must be willing to participate in the pharmacokinetic studies PHASE II Inclusion Criteria (phase II patients must meet the general eligibility criteria as well as the following): - Patients may have had treatment for no more than 2 prior relapses. - It is mandatory that 15 unstained paraffin slides or 1 representative tissue block be available from original surgery or definitive surgery or the surgery closest to initiation of this clinical trial. Exclusion Criteria: - Subject has received previous therapy with anti-VEGF targeted agents or with any histone deacetylase inhibitors. Prior treatment with valproic acid for seizures is allowed but requires a washout of at least 14 days prior to starting LBH589. - Bleeding diathesis or coagulopathy - History of intratumoral or peritumoral hemorrhage if deemed significant by the treating physician - Treatment with warfarin. For patients requiring anticoagulation therapy, only therapeutic low molecular weight heparin or factor Xa inhibitors are permitted. - Patients who have received any investigational drug or undergone major surgery < 4 weeks prior to starting study drug or who have not recovered from side effects of such therapy - Any significant medical illnesses that in the investigator's opinion cannot be adequately controlled with appropriate therapy or would compromise the patient's ability to tolerate this therapy - Patients with any disease that will obscure toxicity or dangerously alter drug metabolism - Patients with a history of any other cancer (except non-melanoma skin cancer or carcinoma in-situ of the cervix), unless in complete remission and has not received treatment for that particular disease for a minimum of 3 years - Impaired cardiac function as described in the protocol - Uncontrolled hypertension and/or prior history of hypertensive crisis or hypertensive encephalopathy - Significant vascular disease within 6 months prior to Day 1 - History of stroke or transient ischemic attack within 6 months prior to Day 1 - Patients with unresolved diarrhea > CTCAE grade 1 - Patients with INR > 1.5 - Patients with major surgery or a significant traumatic injury within 28 days prior to Day 1 - Patients with any condition that impairs their ability to swallow and/or absorb pills - Concomitant use of drugs with a risk of causing torsades de pointes - Concomitant use of CYP3A4 inhibitors during the treatment phase of the study and within 72 hours prior to starting treatment - Concomitant use of any anti-cancer therapy or radiation therapy, or any other investigational agent - Patients has known human immunodeficiency virus (HIV) of hepatitis C infection, baseline treating for HIV or hepatitis C is not required - History of allergic reactions attributed to compounds of similar chemical or biologic composition to LBH589 or bevacizumab, or their excipients - Patient is in a situation or condition that, in the opinion of the investigator, may interfere with optimal participation in the study - Patient has a significant history of non-compliance to medical regimens - Core biopsy or other minor surgical procedure, excluding placement of a vascular access device, within 7 days prior to Day 1 - History of abdominal fistula or gastrointestinal perforation within 6 months prior to Day 1 - Serious, non-healing wound, active ulcer, or untreated bone fracture - Proteinuria as demonstrated by a UPC ration of 1.0 or greater at screening - Subject is pregnant or intends to become pregnant during the study