Clawpack is a library for solving nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. It supports Adaptive Mesh Refinement (AMR), which is essential in solving multi-scale problems. Recently, we added capabilities to accelerate the code by using the Graphics Process Unit (GPU). Routines that manage CPU and GPU AMR data and facilitate the execution of GPU kernels are added. Customized and CPU thread-safe memory managers are designed to manage GPU and CPU memory pools, which is essential in eliminating the overhead of memory allocation and de-allocation. A global reduction is conducted every time step for dynamically adjusting the time step based on Courant number restrictions. Some small GPU kernels are merged into bigger kernels, which greatly reduces kernel launching overhead. A speed-up between $2$ and $3$ for the total running time is observed in an acoustics benchmark problem.