Light field cameras capture both the spatial and the angular properties of light rays in space. Due to its property, one can compute the depth from light fields in uncontrolled lighting environments, which is a big advantage over active sensing devices. Depth computed from light fields can be used for many applications including 3D modelling and refocusing. However, light field images from hand-held cameras have very narrow baselines with noise, making the depth estimation difficult. Many approaches have been proposed to overcome these limitations for the light field depth estimation, but there is a clear trade-off between the accuracy and the speed in these methods. In this paper, we introduce a fast and accurate light field depth estimation method based on a fully-convolutional neural network. Our network is designed by considering the light field geometry and we also overcome the lack of training data by proposing light field specific data augmentation methods. We achieved the top rank in the HCI 4D Light Field Benchmark on most metrics, and we also demonstrate the effectiveness of the proposed method on real-world light-field images.