The Indian summer monsoon (ISM) simulated over the 1989–2009 period with a new 0.75° ocean–atmosphere coupled tropical-channel model extending from 45°S to 45°N is presented. The model biases are comparable to those commonly found in coupled global climate models (CGCMs): the Findlater jet is too weak, precipitations are underestimated over India while they are overestimated over the southwestern Indian Ocean, South-East Asia and the Maritime Continent. The ISM onset is delayed by several weeks, an error which is also very common in current CGCMs. We show that land surface temperature errors are a major source of the ISM low-level circulation and rainfall biases in our model: a cold bias over the Middle-East (ME) region weakens the Findlater jet while a warm bias over India strengthens the monsoon circulation over the southern Bay of Bengal. A surface radiative heat budget analysis reveals that the cold bias is due to an overestimated albedo in this desertic ME region. Two new simulations using a satellite-observed land albedo show a significant and robust improvement in terms of ISM circulation and precipitation. Furthermore, the ISM onset is shifted back by 1 month and becomes in phase with observations. Finally, a supplementary set of simulations at 0.25°-resolution confirms the robustness of our results and shows an additional reduction of the warm and dry bias over India. These findings highlight the strong sensitivity of the simulated ISM rainfall and its onset timing to the surface land heating pattern and amplitude, especially in the ME region. It also illustrates the key-role of land surface processes and horizontal resolution for improving the ISM representation, and more generally the monsoons, in current CGCMs.