Quantitative information on the response of global terrestrial net primary production (NPP) to climate change and increasing atmospheric CO2 is essential for climate change adaptation and mitigation in the 21st century. Using a process-based ecosystem model (the Dynamic Land Ecosystem Model, DLEM), we quantified the magnitude and spatiotemporal variations of contemporary (2000s) global NPP, and projected its potential responses to climate and CO2 changes in the 21st century under the Special Report on Emission Scenarios (SRES) A2 and B1 of Intergovernmental Panel on Climate Change (IPCC). We estimated a global terrestrial NPP of 54.6 (52.8-56.4) PgC yr(-1) as a result of multiple factors during 2000-2009. Climate change would either reduce global NPP (4.6%) under the A2 scenario or slightly enhance NPP (2.2%) under the B1 scenario during 2010-2099. In response to climate change, global NPP would first increase until surface air temperature increases by 1.5 °C (until the 2030s) and then level-off or decline after it increases by more than 1.5 °C (after the 2030s). This result supports the Copenhagen Accord Acknowledgement, which states that staying below 2 °C may not be sufficient and the need to potentially aim for staying below 1.5 °C. The CO2 fertilization effect would result in a 12%-13.9% increase in global NPP during the 21st century. The relative CO2 fertilization effect, i.e. change in NPP on per CO2 (ppm) bases, is projected to first increase quickly then level off in the 2070s and even decline by the end of the 2080s, possibly due to CO2 saturation and nutrient limitation. Terrestrial NPP responses to climate change and elevated atmospheric CO2 largely varied among biomes, with the largest increases in the tundra and boreal needleleaf deciduous forest. Compared to the low emission scenario (B1), the high emission scenario (A2) would lead to larger spatiotemporal variations in NPP, and more dramatic and counteracting impacts from climate and increasing atmospheric CO2.