A compact full-color electro-holographic three-dimensional (3-D) display with undersampled computer-generated holograms (US-CGHs) and oblique projection imaging (OPI) is proposed. For its realization, undersampling conditions of the CGH enabling the complete recovery of image information are derived, and the OPI-based longitudinal-to-lateral depth conversion (LTL-DC) scheme allowing the simple reconstruction of full-color images is also proposed. Three-color off-axis US-CGHs are generated with their center-shifted principle fringe patterns (CS-PFPs) of the novel look-up table (NLUT) method, where center-shifts are calculated with the derived undersampling conditions of the CGH based on the generalized sampling theorem, and then multiplexed into the color-multiplexed hologram (CMH). The CMH is loaded on a SLM (spatial light modulator) and reconstructed by being illuminated with a multi-wavelength light source, where an original full-color image is reconstructed being spatially separated from the other color-dispersed images on the projected image plane with the OPI-based LTL-DC process, which enables us to view the original full-color image just with a simple filter mask. Performance analysis and successful experiments with the test 3-D objects in motion confirm the feasibility of the proposed system.