Simplified Unsymmetrical Multi-Hexagon Search is one of the faster motion estimation algorithms for video coding available in the literature. It achieves a very good tradeoff between computational complexity and coding efficiency. In fact, the H.264/AVC reference software includes it, and it could easily be extended to the new video coding standard: High Efficiency Video Coding. This paper proposes a parallel algorithm which implements the Simplified Unsymmetrical Multi-Hexagon motion search in a graphic processing unit which serves as co-processor for the central processing unit. The results show a negligible rate distortion drop with a speed-up of up to 8× for the motion estimation module compared to the sequential version. Furthermore, the proposed algorithm is evaluated against some related proposals available in the literature, outperforming all of them in terms of time reduction as well as coding efficiency.