This study compares the simulation of tropical convection in the National Center for Atmospheric Research Community Climate Model, version 3 (CCM3), using the original and a revised convective parameterization closure in the Zhang-McFarlane scheme. The revised closure couples convection to the large-scale forcing in the free troposphere instead of to the convective available potential energy in the atmosphere as employed in the original closure. In addition, a relative humidity threshold is used for convection trigger. It is shown that the mean precipitation distribution in the tropical regions for both summer and winter is, in general, improved when the new closure is used. During June, July, and August the precipitation in the western Pacific monsoon region is significantly enhanced, alleviating the negative precipitation bias there in the model. The spurious precipitation in the Arabian Peninsula desert is completely eliminated. During December, January, and February the South Pacific Convergence Zone is enhanced considerably. All these changes are desirable in addressing important model deficiencies. The probability distributions of the precipitation intensity from the model simulations are compared with that from the Tropical Rainfall Measurement Mission (TRMM) data. It is shown that over 90% of the CCM3 precipitation is from light rain with rainfall rate less than 1 mm h-1, whereas the simulation with the new closure and the TRMM observations show significant contribution (30--40%) from rainfall rates greater than 2 mm h-1. Precipitation simulation over the western North Pacific summer monsoon region and the Arabian Peninsula was examined in detail to understand the causes of the precipitation biases in CCM3 over these regions. It is demonstrated that the convective available potential energy (CAPE)-based closure limits the CAPE buildup at the beginning of the monsoon season, resulting in the under simulation of the western North Pacific monsoon precipitation. In the Arabian Peninsula the positive feedback between convection and surface evaporation leads to the spurious heavy precipitation center there. In addition to the new closure the use of relative humidity threshold is also found to be important to the improvement of the simulation.