The new generation video coding standard HEVC has as many as 35 prediction modes and more flexible coding unit (CU) sizes. Although HEVC has better coding performance, it has high computational complexity and long coding time. In real-time signal processing systems, the algorithm must be further optimized. This paper proposes an efficient, fast intra-prediction algorithm for HEVC intra-coding. For the CU size decision, we use the depth information of the adjacent CUs to terminate the division in advance. For the intra-prediction mode selection, we use the parent CU's best prediction mode and the most probable modes (MPMs) to reduce the modes in the rate-distortion optimization process. Experimental results show that the proposed algorithm reduces encoding time by 47.21% on average, BD-BR increases by 1.81%, BD-PSNR decreases by 0.01dB, and SSIM decreases by 0.011. Comparing the proposed algorithm's RD curves with the existing algorithm, the proposed algorithm's rate-distortion performance has not changed significantly. The proposed algorithm does not significantly change the encoding performance and image quality while reducing the encoding time. The research method in this paper has theoretical guiding significance for HEVC intra-coding algorithm.