Multi-view clustering aims to cluster data from diverse sources or domains, which has drawn considerable attention in recent years. In this paper, we propose a novel multi-view clustering method named multi-view spectral clustering network (MvSCN) which could be the first deep version of multi-view spectral clustering to the best of our knowledge. To deeply cluster multi-view data, MvSCN incorporates the local invariance within every single view and the consistency across different views into a novel objective function, where the local invariance is defined by a deep metric learning network rather than the Euclidean distance adopted by traditional approaches. In addition, we enforce and reformulate an orthogonal constraint as a novel layer stacked on an embedding network for two advantages, i.e. jointly optimizing the neural network and performing matrix decomposition and avoiding trivial solutions. Extensive experiments on four challenging datasets demonstrate the effectiveness of our method compared with 10 state-of-the-art approaches in terms of three evaluation metrics.