Screen content coding (SCC) is developed to encode screen content videos, and it is an extension of High Efficiency Video Coding (HEVC). Since screen content videos contain computer-generated content that shows special characteristics, SCC adopts the new Intra Block Copy mode and Palette mode besides the HEVC based Intra mode to improve the coding efficiency. However, the exhaustive mode searching process makes the SCC encoder computational expensive. In this paper, a low-complexity intra prediction algorithm is proposed by the convolutional neural network (CNN). The proposed network skips unnecessary coding units (CUs) and mode candidates by imitating the behavior of the original SCC encoder. The network first decides if a CU size should be checked by analyzing global features, and it decides which mode should be checked by analyzing the local features. Experimental results show that the proposed algorithm achieves 53.44% computational complexity reduction on average with 1.94% Bj⊘ntegaard delta bitrate loss under All Intra configuration.