Multi-view clustering (MvC) aims at exploring the category structure among multi-view data without label supervision. Multiple views provide more information than single views and thus existing MvC methods can achieve satisfactory performance. However, their performance might seriously degenerate when the views are noisy in practical scenarios. In this paper, we first formally investigate the drawback of noisy views and then propose a theoretically grounded deep MvC method (namely MvCAN) to address this issue. Specifically, we propose a novel MvC objective that enables un-shared parameters and inconsistent clustering predictions across multiple views to reduce the side effects of noisy views. Furthermore, a non-parametric iterative process is designed to generate a robust learning target for mining multiple views' useful information. Theoretical analysis reveals that MvCAN works by achieving the multi-view consistency, complementarity, and noise robustness. Finally, experiments on public datasets demonstrate that MvCAN outperforms state-of-the-art methods and is robust against the existence of noisy views.