To increase the coding speed of the quality Scalable High efficiency Video Coding (SHVC), a new intra prediction algorithm based on quality SHVC was proposed. Firstly, the potential depth was predicted by using inter-layer correlation, and the depths with low possibility were eliminated. Secondly, for the likely depth, Inter-Layer Reference (ILR) mode was used to code and examine the residual distribution by using distribution fitting to determine whether the residuals follow a Laplace distribution. If the residual followed the Laplace distribution, intra prediction was skipped. Finally, the depth residual coefficient of depth coding was tested to determine whether to satisfy the depth of early termination, if the condition was met, the code process would be terminated to improve the coding speed. The experimental results show that the proposed algorithm can improve the coding speed by 79% with negligible coding loss.