Developing parallel algorithms for solving large sparse linear systems is an important and challenging task in scientific computing and practical applications. In this work, we develop a new parallel algebraic multigrid (AMG) method for GPU. The coarsening and smoothing procedures in our new algorithm are based on a quadtree (octree in 3D) generated from an auxiliary grid. This provides (nearly) optimal load balance and predictable communication patterns --- factors that make our new algorithm suitable for parallel computing, especially on GPU. Numerical results show that our new method can speed up the existing GPU code (CUSP from NVIDIA) by a factor of 4 on a quasi-uniform grid and by a factor of 2 on a shape-regular grid for certain model problems. This work is co-authored by J. Cohen, L. Wang, and J. Xu.