In this paper,we present a hybrid circular queue method that can significantly boost the performance of stencil computations on GPU by carefully balancing usage of registers and shared-memory.Unlike earlier methods that rely on circular queues predominantly implemented using indirectly addressable shared memory,our hybrid method exploits a new reuse patt spanning across the multiple time steps in stencil computations so that circular queues can be implemented by both shared memory and registers effectively in a balanced manner.We describe a framework that automatically finds the best placement of data in registers and shared memory in order to maximize the performance of stencil computations.Validation using four different types of stencils on three different GPU platforms shows that our hybrid method achieves speedups up to 2.93X over methods that use circular queues implemented with shared-memory only.