By integrating multiple views, i.e., multi-view learning (ML), we can discover the underlying data structures so that the performance of learning tasks can improve. As a basic and important branch of ML, multi-view clustering has achieved great success recently in pattern recognition and machine learning communities. Most existing multi-view spectral clustering methods heavily adopt the relax-and-discretize strategy to obtain discrete cluster labels (clustering results), i.e., using predefined similarity graphs to learn a consensus Laplacian embedding shared by all views for K-means clustering. However, the above clustering strategy may significantly affect clustering performance since there is information loss between independent steps. In this paper, we establish a novel Self-taught Multi-view Spectral Clustering (SMSC) framework to address the above issue. As the main contributions of this paper, we provide two versions of SMSC based on convex combination and centroid graph fusion schemes. Specifically, a self-taught mechanism is introduced in SMSC, which can effectively feedback the manifold structure induced by Laplacian embedding and the cluster information hidden in the discrete indicator matrix to learn an optimal consensus similarity graph for graph partitioning. The effectiveness of the proposed methods has been evaluated on real-world multi-view datasets, and experimental results show that our methods outperform other state-of-the-art baselines.