In this paper, we present a Smoothed Particle Hydrodynamics (SPH) implementation algorithm on GPUs. To compute a force on a particle, neighboring particles have to be searched. However, implementation of a neighboring particle search on GPUs is not straightforward. We developed a method that can search for neighboring particles on GPUs, which enabled us to implement the SPH simulation entirely on GPUs. Since all of the computation is done on GPUs and no CPU processing is needed, the proposed algorithm can exploit the massive computational power of GPUs. Consequently, the simulation speed is many times increased with the proposed method.