This study introduces a simple yet physically-based model for simulating vegetation carbon uptake based on recent hydrological and ecological theories. The model simulates spatially distributed, monthly gross primary productivity (GPP) over the global domain. Two essential concepts underpin this model: i) evapotranspiration (ET) estimation based on the generalized proportionality hypothesis and the abcd model, and ii) a functional relationship between GPP and ET. The WFDEI global forcing dataset was used for the abcd model input and GPP and ET data from FluxCom for calibration and validation. The model parameters are calibrated in two stages: the first stage determines GPP-ET functional relationship parameters, and the second stage estimates abcd model parameters. Furthermore, we used a multilinear regression and machine learning technique to evaluate factors underpinning the GPP-ET functional relationship at the global scale. GPP simulated with optimal parameters obtained from the two stages captured the seasonal patterns and magnitudes of FluxCom GPP reasonably well. The Kling-Gupta-Efficiency (KGE) values were ≥ 0.5 and ≥ 0.8 at 98.5% and 88.4% of the global land grids. This model has excellent fidelity and computational efficiency for simulating monthly GPP globally. It can also be employed for diagnosing coupled hydrologic and ecologic processes in land surface and earth system models.