Among the existing video applications, screen content videos occupy a large proportion. Therefore, how to effectively compress screen content according to its characteristics has been a hot topic in the field of video coding. Since palette mode is a core tool for screen content coding in the Versatile Video Coding (VVC) Standard, it is of great importance to optimize its performance. In this paper, we propose an optimization algorithm for palette color table coding. The algorithm improves the compression performance when encoding the palette color table by introducing two methods, namely differential pulse code modulation and cross-component linear prediction. Experimental results show that the algorithm is able to optimize the coding performance with almost no increase in encoding and decoding time.