Image subspace clustering is an efficient technique for segmenting data into latent subspaces. There are various methods for clustering, and two of them are exemplary: low-rank representation and sparse subspace clustering. The block diagonal is a crucial property in these methods as it results in precise subspace clustering. Additionally, Laplacian regularization is capable of capturing sequential relationships. In this paper, we propose a subspace clustering model utilizing block diagonal and Laplacian regularization. Following this, we present a highly efficient algorithm to solve the model. To segment the subspaces, we construct an affinity graph utilizing a block diagonal matrix via spectral clustering. The effectiveness of our approach is demonstrated through experimental results on three datasets. The proposed method notably enhances the accuracy of clustering, in comparison to the current subspace clustering techniques.