In this paper we propose a novel deep learning-based visual comfort assessment (VCA) for stereoscopic images. To assess the overall degree of visual discomfort in stereoscopic viewing, we devise a binocular fusion deep network (BFN) learning binocular characteristics between stereoscopic images. The proposed BFN learns the latent binocular feature representations for visual comfort score prediction. In the BFN, the binocular feature is encoded by fusing the spatial features extracted from left and right views. Finally, visual comfort score is predicted by projecting the binocular feature onto the subjective score space. In addition, we devise a disparity regularization network (DRN) for improving prediction results. The proposed DRN takes the binocular feature from the BFN and estimates disparity maps from the feature in order to embed disparity relations between left and right views into the deep network. The proposed deep network with BFN and DRN is end-to-end trained in a unified framework where the DRN acts as disparity regularization. We evaluated the prediction performance of the proposed deep network for VCA by the comparison of existing objective VCA metrics. Further, we demonstrated that the proposed BFN showed various factors causing visual discomfort by using network visualization.