It is shown in this study that applying some convection suppression criteria to the MIT or Emanuel cumulus parameterization scheme may significantly improve the performance of a regional climate model to simulate the Asian summer monsoon precipitation, particularly the precipitation over southeastern China and the Mei-yu rainband over the East Asian region. With the original MIT cumulus scheme, the precipitation over the ocean particularly the South China Sea (SCS) region is generally over-estimated, which may result in the under-estimation of precipitation over China. It is found that the relative vorticity criterion (which shuts down the convection when the low-level flow is anticyclonic and stronger than a certain threshold value) has the largest impact on suppressing the over-estimated precipitation over the SCS.