Existing subspace clustering methods typically employ shallow models to estimate underlying subspaces of unlabeled data points and cluster them into corresponding groups. However, due to the limited representative capacity of the employed shallow models, those methods may fail in handling realistic data without the linear subspace structure. To address this issue, we propose a novel subspace clustering approach by introducing a new deep model - Structured AutoEncoder (StructAE). The StructAE learns a set of explicit transformations to progressively map input data points into nonlinear latent spaces while preserving the local and global subspace structure. In particular, to preserve local structure, the StructAE learns representations for each data point by minimizing reconstruction error with respect to itself. To preserve global structure, the StructAE incorporates a prior structured information by encouraging the learned representation to preserve specified reconstruction patterns over the entire data set. To the best of our knowledge, StructAE is one of the first deep subspace clustering approaches. Extensive experiments show that the proposed StructAE significantly outperforms 15 state-of-the-art subspace clustering approaches in terms of five evaluation metrics.