The Asian‐Australian monsoon (AAM) plays a vital role in modulating the global and local climates. Current numerical models, including climate system models (CSMs) and atmospheric general circulation models (AGCMs), have difficulties in capturing the fundamental and intrinsic features of the AAM. By applying the stochastic multicloud model (SMCM) to the state‐of‐the‐art ECHAM6.3 atm model, we investigated the impacts of SMCM on the simulation of AAM precipitation. Though the modified model with the SMCM improves simulations of the AAM precipitation in June–July–August–September season, the solstice mode, the AAM domain, and the AAM precipitation intensity, deficiencies also exist in other aspects, that is, simulations of rainfall in December–January–February–March and April–May seasons, and the equinox mode. Analyses also unravelled the modified model improves in simulating the spatial patterns of seasonal variation of precipitation in the Indian monsoon region, western North Pacific monsoon region, and Australian monsoon region in terms of pattern correlation coefficient and normalized root‐mean square error scores. The enhanced simulation of solar radiation in the modified model favours improving the performance of the simulated solstice mode. In addition, moisture budget analysis was applied to investigate physical processes that modulate the variations and distributions of AAM precipitation. Analyses revealed that variations and distributions of the vertical integral of moisture flux convergence is closely associated with changes in precipitation, while the stratification of vertical moist transport is associated with changes in precipitation over land in the AAM region. In addition, the modified model influences the AAM precipitation mainly through the variations of moisture flux convergence. The present work potentially provides a method to improve the simulated capability of AGCMs.