Climate and physiological controls of vegetation gross primary production (GPP) vary in space and time. In many ecosystems, GPP is primary limited by absorbed photosynthetically-active radiation; in others by canopy conductance. These controls further vary in importance over daily to seasonal time scales. We propose a simple but effective conceptual model that estimates GPP as the lesser of a conductance-limited (Fc) and radiation-limited (Fr) assimilation rate. Fc is estimated from canopy conductance while Fr is estimated using a light use efficiency model. Both can be related to vegetation properties observed by optical remote sensing. The model has only two fitting parameters: maximum light use efficiency, and the minimum achieved ratio of internal to external CO2 concentration. The two parameters were estimated using data from 16 eddy covariance flux towers for six major biomes including both energy- and water-limited ecosystems. Evaluation of model estimates with flux tower-derived GPP compared favourably to that of more complex models, for fluxes averaged; per day (r2 = 0.72, root mean square error, RMSE = 2.48 μmol C m2 s− 1, relative percentage error, RPE = − 11%), over 8-day periods (r2 = 0.78 RMSE = 2.09 μmol C m2 s− 1,RPE = − 10%), over months (r2 = 0.79, RMSE = 1.93 μmol C m2 s− 1, RPE = − 9%) and over years (r2 = 0.54, RMSE = 1.62 μmol C m2 s− 1, RPE = − 9%). Using the model we estimated global GPP of 107 Pg C y− 1 for 2000-2011. This value is within the range reported by other GPP models and the spatial and inter-annual patterns compared favourably. The main advantages of the proposed model are its simplicity, avoiding the use of uncertain biome- or land-cover class mapping, and inclusion of explicit coupling between GPP and plant transpiration.