General Circulation Models (GCMs) for weather forecasts and climate simulations continue having difficulties in modeling the diurnal precipitation, particularly over land. In this study, we revise the convective triggering function used in the DOE’s Energy Exascale Earth System Model (E3SM) Atmosphere Model version 1 (EAMv1) by introducing a simple dynamic constraint on the initiation of convection that emulates the collective effects of lower level moistening and upward motion of the large-scale circulation 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. Based on 11-year AMIP simulations, we find that the revised trigger 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 well captured. The overall impact of the mean precipitation with the revised trigger is minor but positive, with 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.