The RDO (Rate Distortion Optimization) process of HEVC results in good coding efficiency, but relatively requires much encoding time. In order to reduce the encoding time of RDO process, this paper proposes a method of fast intra prediction mode decision using DCT coefficients distributions and the existence of DCT coefficients. The proposed fast Intra coding sets the number of intra prediction mode candidates to three(3) from the RMD (Rough Mode Decision) process in HM16.0 reference SW and reduces the number of candidates one more time by investigating DCT coefficients distribution. After that, if there exists a quantized DCT block having all zero coefficient values for a specific candidate before the RDO process, the candidate is chosen without the RDO process. The proposed method reduces the encoder complexity on average 46%, while the coding efficiency is 2.1% decreased compared with the HEVC encoder.