Multiview clustering refers to partition data according to its multiple views, where information from different perspectives can be jointly used in some certain complementary manner to produce more sensible clusters. It is believed that most of the existing multiview clustering methods technically suffer from possibly corrupted data, resulting in a dramatically decreased clustering performance. To overcome this challenge, we propose a multiview spectral clustering method based on robust subspace segmentation in this article. Our proposed algorithm is composed of three modules, that is: 1) the construction of multiple feature matrices from all views; 2) the formulation of a shared low-rank latent matrix by a low rank and sparse decomposition; and 3) the use of the Markov-chain-based spectral clustering method for producing the final clusters. To solve the optimization problem for a low rank and sparse decomposition, we develop an optimization procedure based on the scheme of the augmented Lagrangian method of multipliers. The experimental results on several benchmark datasets indicate that the proposed method outperforms favorably compared to several state-of-the-art multiview clustering techniques.