High Efficiency Video Coding (HEVC) suffers from high computational complexity due to its quad-tree structure in motion estimation (ME). This paper exposes an adaptive search range decision algorithm for accelerating HEVC integer-pel ME on GPU which estimates the optimal search range (SR) using a MAP (Maximum A Posteriori) estimator. There are three main contributions; First, we define the motion feature as the standard deviation of motion vector difference values in a CTU. Second, a MAP estimator is proposed, which theoretically estimates the motion feature of the current CTU using the motion feature of a temporally adjacent CTU and its SR without any data dependency. Thus, the SR for the current CTU is parallelly determined. Finally, the values of the prior distribution and the likelihood for each discretized motion feature are computed in advance and stored at a look-up table to further save the computational complexity. Experimental results show in conventional HEVC test sequences that the proposed algorithm can achieves high average time reductions without any subjective quality loss as well as with little BD-bitrate increase.