A surface light field represents the radiance of rays originating from any points on the surface in any directions. Traditional approaches require ultra-dense sampling to ensure the rendering quality. In this paper, we present a novel neural network based technique called deep surface light field or DSLF to use only moderate sampling for high fidelity rendering. DSLF automatically fills in the missing data by leveraging different sampling patterns across the vertices and at the same time eliminates redundancies due to the network's prediction capability. For real data, we address the image registration problem as well as conduct texture-aware remeshing for aligning texture edges with vertices to avoid blurring. Comprehensive experiments show that DSLF can further achieve high data compression ratio while facilitating real-time rendering on the GPU.