Summary: Recently, an increasingly pervasive trend in real-word applications is that the data are collected from multiple sources or represented by multiple views. Owing to the powerful ability of affinity graph in capturing the structural relationships among samples, constructing a robust and meaningful affinity graph has been extensively studied, especially in spectral clustering tasks. However, conventional spectral clustering extended to multi-view scenarios cannot obtain the satisfactory performance due to the presence of noise and the heterogeneity among different views. In this paper, we propose a robust affinity graph learning framework to deal with this issue. First, we employ an improved feature selection algorithm that integrates the advantages of hypergraph embedding and sparse regression to select significant features such that more robust graph Laplacian matrices for various views on this basis can be constructed. Second, we model hypergraph Laplacians as points on a Grassmann manifold and propose a Consistent Affinity Graph Learning (CAGL) algorithm to fuse all views. CAGL aims to learn a latent common affinity matrix shared by all Laplacian matrices by taking both the clustering quality evaluation criterion and the view consistency loss into account. We also develop an alternating descent algorithm to optimize the objective function of CAGL. Experiments on five publicly available datasets demonstrate that our proposed method obtains promising results compared with state-of-the-art methods.