The versatile video coding (VVC) is the latest video coding standard, which uses a Multi-Type Tree (MTT) coding structure. Compared with existing video coding standards, this structure can flexibly split coding blocks according to the complex texture features of the image. As MTT structure introduces binary tree (BT) and ternary tree (TT) splitting, it will lead to a sharp increase in computational complexity. In the paper, a fast Coding Unit (CU) size decision method for intra prediction of VVC is proposed, which can significantly reduce the calculation in the intra encoding of VVC. The proposed method consists of two steps: 1) determine whether CU is divided and 2) select the best CU splitting mode. In the intra prediction process, the CU texture complexity is firstly calculated, which judges whether the CU is divided into sub-CUs. Then, the unnecessary splitting mode candidates are discarded according to the relationship between the texture direction and the CU splitting mode. The experimental results show that our proposed fast CU partition method reduces about 48.58% the computational complexity, while the BDBR only increases by 0.91%.