Scalable High Efficiency Video Coding (SHVC) is the extension of High Efficiency Video Coding (HEVC). In intra prediction for quality SHVC, a Coding Unit (CU) is recursively divided into a quadtree-based structure from the largest 64×64 CU to the smallest 8×8 CU, in which 35 intra prediction modes and Inter-Layer Reference (ILR) mode are checked to determine the best possible mode. This leads to very high coding efficiency but also results in an extremely high coding complexity. To improve coding speed while maintaining coding efficiency, in this paper, we propose a new efficient algorithm for fast intra prediction for enhancement layer in SHVC. First, temporal and spatial correlations, as well as their correlation degrees, are combined in a Naive Bayes classifier to predict depth probabilities and skip depths with low likelihood. Second, for a given depth candidate, we combine ILR mode probability with Partial Zero Blocks (PZBs) based on the Sum of Squared Differences (SSD) to determine whether the ILR mode is the best one. In that case, we can skip intra prediction, which requires very high complexity. Third, initial Intra Modes (IMs) are obtained through Sobel operator, and are combined with the relationship between IMs and their corresponding Hadamard Cost (HC) values to predict candidate IMs in Rough Mode Decision (RMD). Then, an analytical criterion of early termination is developed based on the HC values of two neighboring IMs in the Rate-Distortion Optimization (RDO) process. Finally, we combine depth probabilities and the distribution of residual coefficients at the current depth to early terminate depth selection. The proposed scheme can significantly decrease the complexity of depth determination while reducing the complexity of mode decision for a depth candidate. Our experimental results demonstrate that the proposed scheme can achieve a speed up gain of more than 80% in average, while maintaining coding efficiency.