The latest Versatile Video Coding (VVC) standard incorporates a series of effective and complex new intra coding tools, which obtains superior coding efficiency than the High Efficiency Video Coding (HEVC). However, this makes the intra coding more complicated and time-consuming. A fast algorithm for VVC is proposed from two aspects of model selection and early terminating to reduce coding complexity in this paper. The relationship between bins with HOG and intra modes is created for the mode selection, decreasing the planar modes for SATD and RDO. Moreover, we analyze the maximum bins to determine the final modes, and we use the modes of left and upper blocks as a reference for the current CU, which can early terminate RDO. The proposed algorithm is implemented on VVC test model, and the experimental results show that it can achieve 36.61% time savings with only 0.94% BDBR increases averagely, which outperforms other relative existing state-of-the-art methods.