Precise information of word boundary can alleviate the problem of lexical ambiguity to improve the performance of natural language processing (NLP) tasks. Thus, Chinese word segmentation (CWS) is a fundamental task in NLP. Due to the development of pre-trained language models (PLM), pre-trained knowledge can help neural methods solve the main problems of the CWS in significant measure. Existing methods have already achieved high performance on several benchmarks (e.g., Bakeoff-2005). However, recent outstanding studies are limited by the small-scale annotated corpus. To further improve the performance of CWS methods based on fine-tuning the PLMs, we propose a novel neural framework, LBGCN, which incorporates a lexicon-based graph convolutional network into the Transformer encoder. Experimental results on five benchmarks and four cross-domain datasets show the lexicon-based graph convolutional network successfully captures the information of candidate words and helps to improve performance on the benchmarks (Bakeoff-2005 and CTB6) and the cross-domain datasets (SIGHAN-2010). Further experiments and analyses demonstrate that our proposed framework effectively models the lexicon to enhance the ability of basic neural frameworks and strengthens the robustness in the cross-domain scenario.