A fast intra-prediction method is proposed for High Efficiency Video Coding (HEVC) using a fast intra-mode decision and fast coding unit (CU) size decision. HEVC supports very sophisticated intra modes and a recursive quadtree-based CU structure. To provide a high coding efficiency, the mode and CU size are selected in a rate-distortion optimized manner. This causes a high computational complexity in the encoder, and, for practical applications, the complexity should be significantly reduced. In this paper, among the many predefined modes, the intra-prediction mode is chosen without rate-distortion optimization processes, instead using the difference between the minimum and second minimum of the rate-distortion cost estimation based on the Hadamard transform. The experiment results show that the proposed method achieves a 49.04% reduction in the intra-prediction time and a 32.74% reduction in the total encoding time with a nearly similar coding performance to that of HEVC test model 2.1.