High Efficiency Video Coding (HEVC) adopts a quad-tree structured coding unit (CU) and more prediction unit (PU) modes are used in all CU depth levels. These improvements bring better coding performance, but the exhaustive search process for optimal CU and PU selection causes higher computational complexity than earlier standards. To speed up the encoder, this paper proposes a fast intra coding algorithm. Firstly, a fast CU size decision method is introduced, which selects different depth decision methods for each largest coding unit. Secondly, a fast direction mode decision method is proposed. It first compares the direction modes of the parent unit and most probable modes (MPMs) list, and then the first direction mode of rate-distortion optimization (RDO) list is used to early terminate the RDO process. Experimental results show that compared with HM 10.0, the proposed algorithm achieves 47% time reduction, whereas the value of BDBR is only 0.7%.