Cross-component linear model (CCLM) chromaticity prediction is a new technique introduced in Versatile Video Coding (VVC), which utilizes the reconstructed luminance component to predict the chromaticity parts, and can improve the coding performance. However, it increases the coding complexity. In this paper, how to accelerate the chroma intra-prediction process is studied based on texture characteristics. Firstly, two observations have been found through experimental statistics for the process. One is that the choice of the chroma intra-prediction candidate modes is closely related to the texture complexity of the coding unit (CU), and the other is that whether the direct mode (DM) is selected is closely related to the texture similarity between current chromaticity CU and the corresponding luminance CU. Secondly, a fast chroma intra-prediction mode decision algorithm is proposed based on these observations. A modified metric named sum modulus difference (SMD) is introduced to measure the texture complexity of CU and guide the filtering of the irrelevant candidate modes. Meanwhile, the structural similarity index measurement (SSIM) is adopted to help judging the selection of the DM mode. The experimental results show that compared with the reference model VTM8.0, the proposed algorithm can reduce the coding time by 12.92% on average, and increases the BD-rate of Y, U, and V components by only 0.05%, 0.32%, and 0.29% respectively.