There is an emerging need to support water and food policy and decision making at the global and national levels. A systematic tool that is capable of analyzing water-food relationships with high spatial resolutions would be very useful. A GEPIC model has recently been developed by integrating a crop growth model with a Geographic Information System (GIS). The GEPIC model was applied to simulate crop yield and crop water productivity (CWP) for maize at a spatial resolution of 30 arc-minutes on a global scale. A comparison between simulated yields and FAO statistical yields in 124 countries shows a good agreement. The simulated CWP values are mainly in line with the measured values reported in literature. The crop yield and CWP were simulated with the assumption of sufficient water and fertilizer supply, holding other factors unchanged. The simulation results show that many countries have the potentials in achieving high maize yields and CWP. More than 80% of African countries have the potential to double their CWP. This reflects the current poor water and fertilizer management there. The results imply that efforts have to be strengthened to improve water and fertilizer management should the malnutrition be reduced or even eliminated.