As a next-generation video compression standard, High Efficiency Video Coding (HEVC) achieves enhanced coding performance relative to prior standards such as H.264/AVC. In the new standard, the improved intra prediction plays an important role in bit rate saving. Meanwhile, it also involves significantly increased complexity, due to the adoption of a highly flexible coding unit structure and a large number of angular prediction modes. In this paper, we present a low-complexity intra prediction algorithm for HEVC. We first propose a fast preprocessing stage based on a simplified cost model. Based on its results, a fast prediction unit selection scheme reduces the number of prediction unit (PU) levels that requires fine processing from 5 to 2. To supply PU size decision with appropriate thresholds, a fast training method is also designed. Still based on the preprocessing results, an efficient mode selection scheme reduces the maximum number of angular modes to evaluate from 35 to 8. This achieves further algorithm acceleration by eliminating the necessity to perform fine Hadamard cost calculation. We also propose a 32 x 32 PU compensation scheme to alleviate the mismatch of cost functions for large transform units, which effectively improves coding performance for high-resolution sequences. In comparison with HM 7.0, the proposed algorithm achieves over 50% complexity reduction in terms of encoding time, with the corresponding bit rate increase lower than 2.0%. Moreover, the achieved complexity reduction is relatively stable and independent to sequence characteristics.