Multi-view subspace clustering (MvSC) is one of the most effective methods for understanding and processing high-dimensional data. However, existing MvSC methods still have two shortcomings: (1) they adopt the nuclear norm as the low-rank constraint, which makes it impossible to fully exploit the mutually complementary subspace information, and (2) they do not handle disjoint and confounding points carefully, which may degrade the purity and distinctiveness of cross-view fusion. To address these issues, in this paper we propose a novel MvSC model with nonconvex ℓq regularization. Specially, our proposed model can not only effectively capture the intrinsic global low-rank structure, but also accurately cluster disjoint and confounding data samples into corresponding subspaces. Then, an efficient algorithm is developed with convergence guarantee. Furthermore, we prove that the sequence generated by our proposed algorithm converges to the desirable Karush-Kuhn-Tucker (KKT) critical point. Extensive experiments on various datasets verify the superiority of our proposed model. MATLAB code is available at https://github.com/wangzhi-swu/NLRSC-MvSC.