High Efficient Video Coding (HEVC) improves coding efficiency but suffers from high computational complexity due to its quad-tree partitioning structure in motion estimation (ME). In recent development of 3D video technology, depth map from the 3D video provides an intimation of the objects' distance from the projected screen in a 3D scene, which inspires the authors to explore the adaptive search range determination for complexity reduction in HEVC. The proposed algorithm exploits the high temporal correlation between the depth map and the motion in texture. By utilizing this correlation and the potential impact of 3D-to-2D projection, a depth/motion relationship is built for a tailor-made search range with a depth-projected scale factor to skip unnecessary search points in ME. Besides, the proposed ASR algorithm can work well with other fast ME algorithms with up to 53% of average coding time reduction whereas the coding efficiency can be maintained.