Commercial light field cameras provide spatial and angular information, but their limited resolution becomes an important problem in practical use. In this letter, we present a novel method for light field image super-resolution (SR) to simultaneously up-sample both the spatial and angular resolutions of a light field image via a deep convolutional neural network. We first augment the spatial resolution of each subaperture image by a spatial SR network, then novel views between super-resolved subaperture images are generated by three different angular SR networks according to the novel view locations. We improve both the efficiency of training and the quality of angular SR results by using weight sharing. In addition, we provide a new light field image dataset for training and validating the network. We train our whole network end-to-end, and show state-of-the-art performances on quantitative and qualitative evaluations.