 This is a Phase III open-label, single-arm study among recurrent malignant glioma patients. Patients will be treated with Vorinostat in combination with Bevacizumab BV 10 mgkg and Temozolomide T 50 mgm2day BV is administered every 2 weeks. Temozolomide will be taken orally once every day. Vorinostat will be taken orally on days 1-7 and 15-21 of each 28-day cycle. In the phase I portion of this study, the dose of Vorinostat will be escalated in successive cohorts of patients to determine the maximum tolerated dose MTD based on dose-limiting toxicities DLTs. In the phase II portion of this study, the dose of Vorinostat will be the MTD determined in the phase I portion. The primary endpoint of the phase II study is 6-month progression-free survival PFS for recurrent GBM Glioblastoma patients. This study will be conducted at The Preston Robert Tisch Brain Tumor Center at Duke. 