Hyperspectral images (HSIs) contain a large number of mixed pixels due to low spatial resolution, which poses great challenges to the analyses and applications of HSIs. In recent years, convolutional neural networks (CNNs) have attained promising performance in HSI field. However, few CNN-based methods are proposed to solve the hyperspectral unmixing (HU) problem because of insufficient labeled samples. In this paper, we propose a novel unsupervised method, sparsity constrained convolutional autoencoder network (SC-CAE), for the HU problem. The data are preprocessed by principal component analysis (PCA) and then fed into the encoder network to obtain low dimensional representations. The decoder network is to reconstruct the original data from these low dimensional representations. Under the sparse constraint, the endmember matrix and the abundance matrix are obtained after many training epochs. The experiment results on synthetic dataset and real dataset show that our method has evident advantages compared with several state-of-the-art methods.