As an extension of High Efficiency Video Coding (HEVC), the Scalable High Efficiency Video Coding (SHVC) introduces multiple layers with inter-layer predictions, which greatly increases the complexity on top of the already complicated HEVC encoder. In Intra prediction for Quality SHVC, Coding Tree Unit (CTU) allows recursive splitting into four depth levels, which considers 35 Intra prediction modes and interlayer reference (ILR) mode to determine the best possible mode at each depth level. This achieves the highest coding efficiency but incurs a substantially high computational complexity. In this paper, we propose a novel Intra prediction scheme to effectively speed up the enhancement layer Intra-coding in Quality SHVC. The new features of the proposed framework include: First, spatial correlation and its correlation degree are combined to predict most probable depth level candidates. Second, for a given depth candidate, based on the probabilities of the ILR mode, we check the ILR mode by examining the residual distribution based on skewness and kurtosis to determine whether the residuals follow a Gaussian distribution. In that case, the Intra prediction comparisons, which require a high complexity, are skipped. Third, during Intra prediction selection from 35 Intra prediction modes, spatial and inter-layer correlations are combined with the local monotonicity of the Hadamard costs associated with the modes in a small neighborhood, to examine only a portion of Intra prediction modes. Finally, a hypothesis testing on the currently selected depth level is performed to examine whether the residuals present significant differences within their block to early terminate depth selection. The proposed multi-step multistrategy scheme aims to minimize the number of depth selections while greatly reducing the mode decision complexity for a depth candidate in a hierarchical fashion. Our experimental results demonstrate that the proposed scheme can achieve a speedup gain of more than 75% in average on the test video sequences, while maintaining almost the same coding efficiency. .