The climate responses to the Maunder Minimum-type total solar irradiance (TSI) decrease in the pre-industrial (PI) era and IPCC B1 global warming scenario are examined using the NCAR CAM3 coupled with a mixed-layer slab ocean model. The TSI reduction shifts the AO/NAO state to a more negative index, resulting in regional surface air temperature (SAT) change in the model. In addition, the positive sea ice-solar radiation feedback amplifies the surface cooling due to the TSI decrease. The global annual average cooling effect induced by the TSI decrease is reduced to 0.254°C in the B1 scenario from 0.347°C in the PI epoch, this difference being due to both the suppressed sea ice-solar radiation feedback and the stronger greenhouse effect associated with the increase of greenhouse gases. However, regional SAT changes in the B1 scenario are strengthened markedly due to the enhanced negative AO/NAO. The warming in the western Greenland, Central Asia and East Asia will be enhanced in the B1 global warming scenario when the TSI decreases. These differences in response between the B1 and PI scenarios illustrate that the impact of multi-decadal solar variation on climate depends on the atmospheric background trace gas composition. A future solar grand minimum does not offset the CO2-induced warming in the B1 scenario, but through the enhanced negative AO/NAO may indeed amplify the warming in certain regions.