We describe a new application of super-resolution image reconstruction to digital holography which is a technique for three-dimensional information recording and reconstruction. Digital holography has suffered from the low resolution of CCD sensors, which significantly limits the size of objects that can be recorded. The existing solution to this problem is to use optics to bandlimit the object to be recorded, which can cause the loss of details. Here super-resolution image reconstruction is proposed to be applied in enhancing the spatial resolution of digital holograms. By introducing a global camera translation before sampling, a high-resolution hologram can be reconstructed from a set of undersampled hologram images. This permits the recording of larger objects and reduces the distance between the object and the hologram. Practical results from real and simulated holograms are presented to demonstrate the feasibility of the proposed technique.