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Observations show a significant positive correlation between the Atlantic Multidecadal Oscillation (AMO) and the Indian Summer Monsoon (ISM) over the past 100 years. Whether this connection is intrinsic to the climate system or caused by external forcing remains unclear in view of the substantial existence of anthropogenic greenhouse gases and aerosols in observations. Two state-of-the-art climate models (GFDL-CM3 and HadGEM2-ES), the historical simulations (1850-2005) of which show positive correlations between the AMO and ISM, similar to observation, are used to address this question. A significant positive AMO-ISM correlation exists in the control simulations with fixed preindustrial forcing with HadGEM2-ES, but not with GFDL-CM3. An in-depth analysis illustrates that the positive correlation in the HadGEM2-ES control run is more reasonable, since it simulates a similar teleconnection of the AMO with the North Pacific to that in both observations and previous studies. In comparison, the GFDL-CM3 control run fails to simulate the teleconnection of the AMO with the North Pacific. The positive AMO-ISM correlation in the historical simulation in GFDL-CM3 may be attributable to the role of the external forcing, since it is so strong that the AMO signals are excited additionally in the North Pacific. This study suggests that the AMO-ISM connection is intrinsic to the climate system, and highlights the crucial role played by the North Pacific in bridging such a connection.