Deep convolutional neural networks (CNNs) have shown great potential to provide accurate depth estimation based on stereo images. Previous work has focused on developing robust stereo matching architectures, while little attention has been paid on improving the network efficiency. In this paper, we propose an efficient Siamese CNN architecture that combines the low resolution disparity estimation and the depth discontinuity aware super-resolution. Specifically, we propose to construct, filter and perform regression on a low resolution cost volume through the designed stereo matching backbone network. A fast depth discontinuity aware super-resolution subnetwork is proposed for upsampling the low resolution disparity map to the desired resolution. Under the guidance of the intensity edge features extracted from the left color image, depth edge residuals are hierarchically learned to refine the upsampled depth map. A delayed upsampling structure is designed to ensure that the computational complexity is proportional to the spatial size of the input disparity map. We also propose to supervise the first derivative loss of the predicted disparity map that makes the network adaptively aware of the depth discontinuity edges. Experiments show that the proposed stereo matching network achieves a comparable prediction accuracy and much faster running speed compared with state-of-the-art methods. INDEX TERMS Stereo matching network, disparity estimation, depth map super-resolution, depth discontinuity aware loss.