General Circulation Models (GCMs) for weather forecasts and climate simulations continue having difficulties in modeling the diurnal precipitation, particularly over land. Most models tend to rain too early after sunrise with a rainfall maximum around the local noon rather than the observed late afternoon peak and fail to capture the observed nocturnal peak. In general, GCMs often rain too frequently at reduced intensity. Increasing model horizontal resolution seems to have little impact on the simulated phase of the diurnal cycle of precipitation. In this study, we proposed a new convective triggering function for weather and climate models by introducing a simple dynamic constraint on the initiation of convection that emulates the collective effects of the large-scale forcing to prevent convection from being triggered too frequently, as well as allowing air parcel launching above boundary layer to capture nocturnal elevated convection which is often decoupled from the surface. The proposed triggering mechanisms have been strongly supported by both field observations and NWP re-analysis in several examined climate regimes. Implementation of the new trigger to the DOE’s Energy Exascale Earth System Model (E3SM) Atmosphere Model version 1 has led to a substantial improvement in the simulated diurnal cycle of precipitation over both midlatitude and tropical lands. The nocturnal peak of precipitation over the central Great Plains and the eastward propagation of convection over the downstream of the Rockies and the adjacent Great Plains are much better captured. The proposed trigger also results in a considerable reduction of convective precipitation over subtropical regions and the frequency of light precipitation occurrence. The overall impact of the mean precipitation with the new trigger is minor with some notable improvements seen over the Indo-Western Pacific, subtropical Pacific and Atlantic, CONUS, and South America. The respective contributions from the individual changes in the convective trigger are discussed.