This paper presents a novel clustering method, named Laplacian regularized deep subspace clustering (LRDSC), for unsupervised hyperspectral image (HSI) classification. We introduce the Laplacian regularization into the subspace clustering to consider the manifold structure reflecting geometric information. To enable the subspace clustering, which works in linear space, to deal with the complicated HSI data with nonlinear characteristics, we combine the subspace clustering as a self-expressive layer with deep convolutional auto-encoder. Furthermore, the 3-D convolutions and deconvolutions with skip connections are utilized to make full extraction of the spectral-spatial information and full use of the historical feature maps produced by the network. We compare the results of the proposed method with six existing cluster methods on four real hyperspectral data sets, showing that the proposed method is able to achieve state-of-the-art performance.