This research presents an adaptive fast motion estimation (ME) computation on the stage of uneven multi-hexagon grid search (UMHGS) algorithm included in an unsymmetrical-cross multi-hexagon-grid search (UMHexagonS) in H.264 standard. The proposed adaptive method is based on statistical analysis and previously obtained motion vectors to reduce the computational complexity of ME. For this purpose, the algorithm is decomposed into three processes: skipping, terminating, and reducing search areas. Skipping and terminating are determined by the statistical analysis of the collected minimum SAD (sum of absolute difference) and the search area is constrained by the slope of previously obtained motion vectors. Simulation results show that 13%-23% of ME time can be reduced compared with UMHexagonS, while still maintaining a reasonable PSNR (peak signal-to-noise ratio) and average bitrates.