Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is smaller than the ambient dimension. Traditional subspace clustering methods often rely on the self-expressiveness property, which has proven effective for linear subspace clustering. However, they perform unsatisfactorily on real data with complex nonlinear subspaces. More recently, deep autoencoder based subspace clustering methods have achieved success owning to the more powerful representation extracted by the autoencoder network. Unfortunately, these methods only considering the reconstruction of original input data can hardly guarantee the latent representation for the data distributed in subspaces, which inevitably limits the performance in practice. In this paper, we propose a novel deep subspace clustering method based on a latent distribution-preserving autoencoder, which introduces a distribution consistency loss to guide the learning of distribution-preserving latent representation, and consequently enables strong capacity of characterizing the real-world data for subspace clustering. Experimental results on several public databases show that our method achieves significant improvement compared with the state-of-the-art subspace clustering methods.