Graph-based multi-view clustering (G-MVC) constructs a graphical representation of each view and then fuses them to a unified graph for clustering. Though demonstrating promising clustering performance in various applications, we observe that their formulations are usually non-convex, leading to a local optimum. In this paper, we propose a novel MVC algorithm termed robust graph-based multi-view clustering (RG-MVC) to address this issue. In particular, we define a min-max formulation for robust learning and then rewrite it as a convex and differentiable objective function whose convexity and differentiability are carefully proved. Thus, we can efficiently solve the resultant problem using a reduced gradient descent algorithm, and the corresponding solution is guaranteed to be globally optimal. As a consequence, although our algorithm is free of hyper-parameters, it has shown good robustness against noisy views. Extensive experiments on benchmark datasets verify the superiority of the proposed method against the compared state-of-the-art algorithms. Our codes and appendix are available at https://github.com/wx-liang/RG-MVC.