Block-diagonal representation (BDR) is an effective subspace clustering method. The existing BDR methods usually obtain a self-expression coefficient matrix from the original features by a shallow linear model. However, the underlying structure of real-world data is often nonlinear, thus those methods cannot faithfully reflect the intrinsic relationship among samples. To address this problem, we propose a novel latent BDR (LBDR) model to perform the subspace clustering on a nonlinear structure, which jointly learns an autoencoder and a BDR matrix. The autoencoder, which consists of a nonlinear encoder and a linear decoder, plays an important role to learn features from the nonlinear samples. Meanwhile, the learned features are used as a new dictionary for a linear model with block-diagonal regularization, which can ensure good performances for spectral clustering. Moreover, we theoretically prove that the learned features are located in the linear space, thus ensuring the effectiveness of the linear model using self-expression. Extensive experiments on various real-world datasets verify the superiority of our LBDR over the state-of-the-art subspace clustering approaches.