In Chinese dependency parsing, the joint model of word segmentation, POS tagging and dependency parsing has become the mainstream framework because it can eliminate error propagation and share knowledge, where the transition-based model with feature templates maintains the best performance. Recently, the graph-based joint model (Yan et al., 2019) on word segmentation and dependency parsing has achieved better performance, demonstrating the advantages of the graph-based models. However, this work can not provide POS information for downstream tasks, and the POS tagging task was proved to be helpful to the dependency parsing according to the research of the transition-based model. Therefore, we propose a graph-based joint model for Chinese word segmentation, POS tagging and dependency parsing. We designed a charater-level POS tagging task, and then train it jointly with the model of Yan et al. (2019). We adopt two methods of joint POS tagging task, one is by sharing parameters, the other is by using tag attention mechanism, which enables the three tasks to better share intermediate information and improve each other’s performance. The experimental results on the Penn Chinese treebank (CTB5) show that our proposed joint model improved by 0.38% on dependency parsing than the model of Yan et al. (2019). Compared with the best transition-based joint model, our model improved by 0.18%, 0.35% and 5.99% respectively in terms of word segmentation, POS tagging and dependency parsing.