The video coding standard H.264 supports video compression with a higher coding efficiency than previous standards. However, this comes at the expense of an increased encoding complexity, in particular for motion estimation which becomes a very time consuming task even for today's central processing units (CPU). On the other hand, modern graphics hardware includes a powerful graphics processing unit (GPU) whose computing power remains idle most of the time. In this paper, we present a GPU based approach to motion estimation for the purpose of H.264 video encoding. A small diamond search is adapted to the programming model of modern GPUs to exploit their available parallel computing power and memory bandwidth. Experimental results demonstrate a significant reduction of computation time and a competitive encoding quality compared to a CPU UMHexagonS implementation while enabling the CPU to process other encoding tasks in parallel.