An accurate estimation of evapotranspiration (ET) is vital for understanding the global hydrological cycle. However, large uncertainties in the present global ET products originate from the distinct model structures, assumptions, and inputs. The maximum entropy production (MEP) model provides a novel method for modeling ET based on parsimonious inputs and energy conservation. In this study, an R package for MEP (RMEP) was presented to facilitate MEP model implementation. Based on RMEP, a global ET analysis was conducted using inputs from the Global Land Data Assimilation System (GLDAS) and Global Land Surface Satellite (GLASS) products during 1978–2018, and the Mann-Kendall and Theil–Sen's methods were employed to detect the ET trends. The MEP-estimated average annual global land ET was 517 mm yr−1 during 1978–2018, and showed a close agreement with eddy-covariance (EC) measurements from 475 flux sites, with a correlation coefficient of 0.74 and root-mean-square error of 26.99 mm mon−1. The overall performance of MEP was evaluated across various land covers, and a higher ET accuracy was revealed for forestlands, wetlands, and cropland land covers. The MEP-derived ET trend corresponded well with the EC-observed ET trend, and the results indicated that the global land ET declined continuously during 1999–2018. Overall, the MEP model provided an accurate ET estimate with parsimonious inputs, which outperformed the GLDAS-Noah ET product and can serve as a global analytical method for the hydrological cycle and climate change.