© Author(s) 2020. 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 GPP (photosynthesis per unit ground area) model, the P-model, that combines the Farquhar-von Caemmerer-Berry model for C3 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 C3 vegetation type. The model builds on the theory developed in

Prentice et al. (

2014) and

Wang et al. (

2017a) and is extended to include low temperature effects on the intrinsic quantum yield and an empirical soil moisture stress factor. The model is forced with site-level data of the fraction of absorbed photosynthetically active radiation (fAPAR) and 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, the

*R*2 is reduced to 0.70 when not accounting for the reduction in quantum yield at low temperatures and effects of low soil moisture on LUE. The

*R*2 for the P-model-predicted LUE is 0.32 (means by site) and 0.48 (means by vegetation type). Applying this model for global-scale simulations yields a total global GPP of 106-122 Pg C yr-1 (mean of 2001-2011), depending on the fAPAR forcing data. The P-model provides a simple but powerful method for predicting-rather than prescribing-light use efficiency and simulating terrestrial photosynthesis across a wide range of conditions. The model is available as an R package (rpmodel).