We present a velocity-map imaging (VMI) apparatus coupled with a magneto-optical trap (MOT) of 87Rb atoms designed for low-energy photo-ion spectroscopy. The VMI-electrode geometry uses a three-electrode configuration, and the focusing electric field is optimized based on systematic simulations of relatively low-energy ions. To calibrate the apparatus, we use resonant two-color two-photon ionization of rubidium atoms as Doppler-selected ions. This VMI system provides an accuracy of 0.15 m/s and a resolution of 7.5 m/s for photoions with speeds below 100 m/s. Finally, details of the design, construction, and testing of the VMI-MOT system are presented.