Recently grid-based physical simulations with multiple GPUs require effective methods to adapt grid resolution to certain sensitive regions of simulations. In multiple GPU computation, an adaptive mesh refinement (AMR) method is one of the effective methods to compute certain local regions that demand higher accuracy with higher resolution. The AMR method on the GPU is, however, complicated and it is necessary to apply various optimizations suitable for GPU in order to obtain high performance. To develop the applications adopting the AMR method effectively with maintaining high performance on GPU, we are developing a block-based AMR framework for stencil applications written in C++ and CUDA. Programmers just write the stencil functions that update a grid point on Cartesian grid. The framework executes these functions over a tree-based AMR data structure effectively. It also provides the efficient GPU-suitable methods for halo exchange and mesh refinement. In this talk, we will explain the implementation and programming model of the proposed AMR framework, and show some computational results on GPU.