The die-stacking DRAM cache can be used to increase bandwidth and reduce latency compared with conventional DRAM memory. However, energy becomes an inevitable challenge with the increasing size of DRAM cache. STT-RAM with near-zero leakage can be integrated with DRAM cache as a hybrid cache to reduce static energy, but the high write energy of STT-RAM brings another energy challenge. In this paper, we propose a tri-regional hybrid cache that can exploit the advantage of both DRAM and STT-RAM technologies. The asymmetric data access policy is introduced based on the non-uniform read/write property of the different hybrid cache regions. We also propose a prediction table that can reduce the searching energy of the hybrid cache. The results show that our hybrid cache reduces energy by 26% and improves performance by 11% on average compared with previous work.