To expedite UHD (Ultra High Definition) video service, the HEVC (High-Efficiency Video Coding) technology has recently been standardized and it achieves two times higher compression efficiency than the conventional H.264/AVC. To obtain the improved efficiency, however, it employs many complex methods which need complicated calculation, thereby resulting in a significantly increased computational complexity when compared to that of H.264/AVC. For example, to improve the coding efficiency of intra frame coding, up to 35 intra prediction modes are defined in HEVC, but this results in an increased encoding time than the H.264/AVC. In this paper, we propose a fast intra prediction mode decision scheme which reduces computational complexity by changing the number of intra prediction mode in accordance with the percentage of PU sizes for a given video resolution, and by classifying the 35 intra prediction modes into 4 categories considering video resolution and quantization parameter. The experimental results show that the total encoding time is reduced by about 7% on average at the cost of only 2% increase in BD-rate.