Chinese word segmentation and dependency parsing are two fundamental tasks for Chinese natural language processing. The dependency parsing is defined at the word-level. Therefore word segmentation is the precondition of dependency parsing, which makes dependency parsing suffer from error propagation and unable to directly make use of character-level pre-trained language models (such as BERT). In this paper, we propose a graph-based model to integrate Chinese word segmentation and dependency parsing. Different from previous transition-based joint models, our proposed model is more concise, which results in fewer efforts of feature engineering. Our graph-based joint model achieves better performance than previous joint models and state-of-the-art results in both Chinese word segmentation and dependency parsing. Additionally, when BERT is combined, our model can substantially reduce the performance gap of dependency parsing between joint models and gold-segmented word-based models. Our code is publicly available at https://github.com/fastnlp/JointCwsParser