<p>Terrestrial photosynthesis is the basis for vegetation growth and drives the land carbon cycle. Accurately simulating gross primary production (GPP, ecosystem-level apparent photosynthesis) is key for satellite monitoring and Earth System Model predictions under climate change. While robust models exist for describing leaf-level photosynthesis, predictions diverge due to uncertain photosynthetic traits and parameters which vary on multiple spatial and temporal scales. Here, we describe and evaluate a gross primary production (GPP, photosynthesis per unit ground area) model, the P-model, that combines the Farquhar-von Caemmerer-Berry model for C<sub>3</sub> photosynthesis with an optimality principle for the carbon assimilation-transpiration trade-off, and predicts a multi-day average light use efficiency (LUE) for any climate and C<sub>3</sub> vegetation type. The model is forced here with satellite data for the fraction of absorbed photosynthetically active radiation and site-specific meteorological data and is evaluated against GPP estimates from a globally distributed network of ecosystem flux measurements. Although the P-model requires relatively few inputs and prescribed parameters, the <i>R</i><sup>2</sup> for predicted versus observed GPP based on the full model setup is 0.75 (8-day mean, 131 sites) – better than some state-of-the-art satellite data-driven light use efficiency models. The <i>R</i><sup>2</sup> is reduced to 0.69 when not accounting for the reduction in quantum yield at low temperatures and effects of low soil moisture on LUE. The <i>R</i><sup>2</sup> for the P-model-predicted LUE is 0.37 (means by site) and 0.53 (means by vegetation type). The P-model provides a simple but powerful method for predicting – rather than prescribing – light use efficiency and simulating terrestrial photosythesis across a wide range of conditions. The model is available as an R package (<i>rpmodel</i>).</p>