Screen content has different characteristics compared with natural content captured by cameras. To achieve more efficient compression, some new coding tools have been developed in the High Efficiency Video Coding (HEVC) Screen Content Coding (SCC) Extension, which also increase the computational complexity of encoder. In this paper, complexity analysis are first conducted to explore the distribution of complexities. Then, two classification trees, including early coding units (CU) partition tree (EPT) and CU content classification tree (CCT), are designed based on statistical characteristics and coding information. EPT is used to decide whether the CU skip the mode decision process of current depth level and CCT is used to classify the blocks into either natural blocks or screen blocks. Natural blocks will skip screen coding modes and screen blocks skip normal intra modes. Experimental results show the proposed algorithm can save 49\% encoding time with 2.7\% BD-rate increase on average for All Intra configuration under the SCC common test condition.