Evapotranspiration is an essential element of the hydrological process. This study derived the long-term series of evapotranspiration from 1982 to 2014 over the three basins, namely source regions of the Yangtze River (SRYR), the Huang River (SRHR) and the Lancang River (SRLR) in the Three-River Source Region of China by integrating multiple sources of evapotranspiration estimates based on the Bayesian model averaging approach, which made full use of the strengths of land surface models and satellite-based products to constrain uncertainties. Then, we analyzed the influences of climate change on evapotranspiration based on the partial least squares regression model. Results indicate that (1) the agreement between various evapotranspiration products and water balance-derived evapotranspiration estimates varies from region to region in the Three-River Source Region of China; (2) annual evapotranspiration increases in the SRYR (3.3±0.8 mm/yr) and the SRHR (0.8±0.4 mm/yr), whereas no significant trends are observed in the SRLR during 1982–2014; (3) annual evapotranspiration is found most sensitive to precipitation and temperature in the SRYR and the SRHR, while it is dominated by relative humidity and temperature in the SRLR during 1982–2014. Our results have important implications for understanding evapotranspiration variability and future water security in the context of global climate change.