The parametric dependence of terrestrial planetary atmospheric circulations and climates on characteristic parameters is studied. A simplified general circulation model—PUMA is employed to investigate the dynamic effects of planetary rotation rate and equator-to-pole temperature difference on the circulation and climate of terrestrial planetary atmospheres. Five different types of circulation regime are identified by mapping the experimental results in a 2-D parameter space defined by thermal Rossby number and frictional Taylor number. The effect of the transfer and redistribution of radiative energy is studied by building up a new two-band semi-gray radiative-convective scheme, which is capable of modelling greenhouse and anti-greenhouse effects while keeping the tunable parameters as few as possible. The results will provide insights into predicting the habitability of terrestrial exoplanets.