Digital holographic imaging is a powerful technique that can provide wavefront information of a three-dimensional object for biological and industrial applications. However, due to the constraint and cost of imaging sensors, the acquired digital hologram is limited in terms of pixel count, thus affecting the resolution in holographic reconstruction. To overcome this constraint, in this paper we propose a deep learning-based method to super-resolve holograms and to improve the quality of low-resolution holograms by training a convolutional neural network with large-scale data for resolution enhancement. Moreover, this algorithm can be broadly adapted to enhance the space-bandwidth product of a holographic imaging system without the need of any advanced hardware. We experimentally validate its capability using a lens-free off-axis holographic system, and compare the performance of various loss functions and interpolation methods in training such a network.