Most existing multi-view subspace clustering approaches only capture the inter-view similarities between different views and ignore the optimal local geometric structure of the original data. To this end, in this letter, we put forward a novel method named shared latent embedding learning for multi-view subspace clustering (SLE-MSC), which can efficiently capture a better latent space. To be specific, we introduce a pseudo-label constraint to capture the intra-view similarities within each view. Meanwhile, we utilize a novel optimal graph Laplacian to learn the consistent latent representation, in which the common manifold is considered as the optimal manifold to obtain a more reasonable local geometric structure. Comprehensive experimental results indicate the superiority and effectiveness of the proposed method.