The simulation of the Indian summer monsoon and its pronounced intraseasonal component in a modern climate model remains a significant challenge. Recently, using observations and reanalysis products, the central Indian Ocean (CIO) mode was found to be a natural mode in the ocean‐atmosphere coupled system and also shown to have a close mechanistic connection with the monsoon intraseasonal oscillation (MISO). In this study, the simulation of the actual CIO mode in historical Community Earth System Model (CESM) outputs is assessed by comparing with observations and reanalysis products. The simulation of the Madden‐Julian Oscillation, a major component of tropical intraseasonal variabilities (ISVs), is satisfactory. However, the CIO mode is not well captured in any of the CESM simulations considered here. The force and response relationship between the atmosphere and the ocean associated with the CIO mode in CESM is opposite to that in nature. The simulated meridional gradient of large‐scale zonal winds is too weak, which precludes the necessary energy conversion from the mean state to the ISVs and cuts off the energy source to MISO in CESM. The inability of CESM to reproduce the CIO mode seen clearly in nature highlights the CIO mode as a new dynamical framework for diagnosing the deficiencies in Indian summer monsoon simulation in climate models. The CIO mode is a coupled metric for evaluating climate models and may be a better indicator of a model's skill to accurately capture the tropical multiscale interactions over subseasonal to interannual timescales.