In this paper, a new deep incomplete multi-view clustering network, called DIMC-net, is proposed to address the challenge of multi-view clustering on missing views. In particular, DIMC-net designs several view-specific encoders to extract the high-level information of multiple views and introduces a fusion graph based constraint to explore the local geometric information of data. To reduce the negative influence of missing views, a weighted fusion layer is introduced to obtain the consensus representation shared by all views. Moreover, a clustering layer is introduced to guarantee that the obtained consensus representation is the best one for the clustering task. Compared with the existing deep learning based approaches, DIMC-net is more flexible and efficient since it can handle all kinds of incomplete cases and directly produce the clustering results. Experimental results show that DIMC-net achieves significant improvement over state-of-the-art incomplete multi-view clustering methods.