High Efficiency Video Coding (HEVC), the latest video coding standard, has twice of the compression efficiency compared to AVC/H.264 under the same image quality condition. To obtain the improved efficiency, however, it was adopted for many methods which need complicated calculation, and the time complexity of HEVC was increased more than that of AVC/H.264. To solve this problem, the various fast algorithms have been researched. In this paper, we propose a fast intra prediction mode decision method which uses result of Rough Mode Decision (RMD) and Most Probable Mode (MPM). The proposed method selects a best predicted mode by comparing each predicted directions which are calculated through RMD and MPM. We applied the proposed method to HM 10.0 and conducted an comparing experiment in All-Intra environment. The experiment result showed that total encoding time is reduced by about 26% on average with about a 0.8% loss of BD-rate.