We present a deep convolutional neural network (CNN) architecture for high-precision depth estimation by jointly utilizing sparse 3D LiDAR and dense stereo depth information. In this network, the complementary characteristics of sparse 3D LiDAR and dense stereo depth are simultaneously encoded in a boosting manner. Tailored to the LiDAR and stereo fusion problem, the proposed network differs from previous CNNs in the incorporation of a compact convolution module, which can be deployed with the constraints of mobile devices. As training data for the LiDAR and stereo fusion is rather limited, we introduce a simple yet effective approach for reproducing the raw KITTI dataset. The raw LiDAR scans are augmented by adapting an off-the-shelf stereo algorithm and a confidence measure. We evaluate the proposed network on the KITTI benchmark and data collected by our multi-sensor acquisition system. Experiments demonstrate that the proposed network generalizes across datasets and is significantly more accurate than various baseline approaches.