Recently, general-purpose graphics processing units (GPGPUs) have been widely used to accelerate computing in various applications. To store the contexts of thousands of concurrent threads on a GPU, a large static random-access memory (SRAM)-based register file is employed. Due to high leakage power of SRAM, the register file consumes 20% to 40% of the total GPU power consumption. Thus, hybrid memory system, which combines SRAM and the emerging non-volatile memory (NVM), has been employed for register file design on GPUs. Although it has shown strong potential to alleviate the power issue of GPUs, existing hybrid memory solutions might not exploit the intrinsic feature of GPU register file. By leveraging the warp schedule on GPU, this paper proposes a hybrid register architecture which consists of a NVM-based register file and mixed SRAM-based write buffers with a warp-aware write back strategy. Simulation results show that our design can eliminate 64% of write accesses to NVM and reduce power of register file by 66% on average, with only 4.2% performance degradation. After we apply the power gating technique, the register power is further reduced to 25% of SRAM counterpart on average.