In order to reduce the encoding complexity of the emerging High Efficiency Video Coding (HEVC), a fast hierarchical algorithm based on texture property and spatial correlation for intra coding was proposed. Firstly, Largest Coding Unit (LCU) level fast algorithm was adopted. The prediction depth of current LCU was derived by weighted prediction using the depth level of neighboring LCUs; the texture complexity of current LCU was determined by means of standard deviation and the strategy of adaptive threshold. Therefore, the Most Probable Depth Range (MPDR) of current LCU could be predicted by combining the prediction depth with the texture complexity of current LCU. Secondly, using Coding Unit (CU) level Depth Decision Fast Algorithm (CUDD-FA), combining the strategy of early decision of CU depth level based on edge-map with early termination of CU depth based on Rate Distortion (RD) cost correlation, the depth level of CU was determined before coding, and the complexity of intra coding process was further reduced. The experimental results show that, compared with the original HEVC encoding scheme, the proposed method reduces encoding time by an average of 41.81%, while the BD-rate (Bjøntegaard Delta bit rate) only increases by 0.74% and the BD-PSNR (Bjøntegaard Delta Peak Signal-to-Noise Rate) only decreases by 0.038 dB; compared with the representative literature algorithms, the proposed algorithm achieves better RD performance with saving more encoding time. The proposed method can significantly reduce the complexity of intra coding process in the premise of negligible RD performance loss, especially for video sequences with high resolution, which is beneficial to the real-time video applications of HEVC standard.