We tentatively analyzed differences between global terrestrial net primary productivity(NPP) under global warming by the targeting temperature of the Pairs Agreement and that during 1986-2005. We addressed the changes in global terrestrial NPP, changes inrelating environmental factors(atmospheric CO_2 concentration, temperature, precipitation, and radiation), and their contribution to the NPP changes under global warming of 1.5℃ and 2℃. The projected global terrestrial NPP increases in proportion to the warming magnitude based on the results from CMIP5 models that runs under the three representative concentration pathways(RCP2.6, RCP4.5 and RCP8.5). Changes in the projected environmental factors and NPP at given warming magnitude are generally consistent across the three RCPs. The increasing atmospheric CO_2 concentration is the dominant factor that drives the total amount of global terrestrial NPP, while the contributions of other environmental factors are relatively small. The most notable increases in NPP locate in southeast China, central Africa, southeast U.S. and western Amazonia. The spatial pattern of NPP changes are mainly controlled by atmospheric CO_2 concentration increase and warming, while precipitation and radiation contribute much fewer. The effects of increasing atmospheric CO_2 concentration on NPP are stronger at lower latitudes but weaker at northern high latitudes. Warming benefits ecosystem NPP at northern high latitudes and Tibetan Plateau but strongly depletes ecosystem NPP at lower latitudes. Our analyses of global terrestrial ecosystem NPP changes under future global warming scenarios still have significant uncertainties due to limitations of current RCPs and earth system models, which needs further refinements.