Graph-based learning approaches have achieved remarkable success in clustering prevalent multi-view data owing to their capacities to reveal the relation between data and discover its underlying structure. However, real multi-view data is not only simply high-dimensional, but also contains noise and redundant information, so the learned affinity graphs may be unreliable, let alone optimal, and produce inaccurate clustering results. Moreover, existing graph learning based multi-view projection models only learn a common graph or a shared low-dimensional embedding matrix, which fails to preserve the flexible local manifold geometry of each view. To alleviate these problems, a novel consensus graph-based auto-weighted multi-view projection clustering (CGAMPC) is developed, which performs dimensionality reduction, manifold structure preservation and consensus structured graph learning simultaneously. To be specific, the ℓ2,1-norm is leveraged to resist noise and adaptively select discriminative features. Meanwhile, to preserve the manifold structure information of all views, we construct informative similarity graphs for the projection data, and fuse them into a consensus structured graph via an auto-weighted synthesis strategy. Furthermore, an effective alternating iterative algorithm is presented to optimize our CGAMPC. Finally, numerical studies on several multi-view benchmark datasets justify the superiority of the proposed approach over other state-of-the-art clustering approaches.