A critical question for agricultural production and food security is how water demand for staple crops will respond to climate and carbon dioxide (CO2) changes1, especially in light of the expected increases in extreme heat exposure2. To quantify the trade-offs between the effects of climate and CO2 on water demand, we use a ‘sink-strength’ model of demand3,4 which relies on the vapour-pressure deficit (VPD), incident radiation and the efficiencies of canopy-radiation use and canopy transpiration; the latter two are both dependent on CO2. This model is applied to a global data set of gridded monthly weather data over the cropping regions of maize, soybean, wheat and rice during the years 1948–2013. We find that this approach agrees well with Penman–Monteith potential evapotranspiration (PM) for the C3 crops of soybean, wheat and rice, where the competing CO2 effects largely cancel each other out, but that water demand in maize is significantly overstated by a demand measure that does not include CO2, such as the PM. We find the largest changes in wheat, for which water demand has increased since 1981 over 86% of the global cropping area and by 2.3–3.6 percentage points per decade in different regions.