The total mass of the atmosphere (or equivalently, the background surface pressure, SP) may have varied significantly over the evolutionary histories of Earth and other planets. Atmospheric mass can affect climate by modifying physical processes, including shortwave scattering, the emissivity of greenhouse gases, the atmospheric heat capacity, and surface fluxes. We apply a three-dimensional global climate model to explore the dependence of climate on SP over the range of 0.5 bar to 2.5 bar. Our simulations show an intriguing, nonmonotonic dependence of climate on SP. Over the SP range of 0.5 bar to 0.9 bar and 1.5 bar to 2.5 bar, the surface temperature increases with SP, however, over the SP range of 0.9 bar to 1.5 bar, the surface temperature decreases with SP. The negative correlation is due to a convection-circulation-cloud coupled feedback. As SP increases, the moist adiabatic lapse rate increases, leading to upper-troposphere cold anomalies in the tropics and middle latitudes that increase the mid-latitude baroclinicity and eddy activity. In association with these changes, the eddy-driven jet is strengthened and shifts equatorward, and two separate westerly jets merge into a single jet. These abrupt circulation changes result in an equatorward shift of the mid-latitude cloud belt and reduction of polar clouds, which induce strong negative cloud radiative forcing that cools the climate. Our results demonstrate that the regime transition of flow state (e.g., the merge of jets here) may induce large anomalies in clouds and radiative forcing, resulting in nonlinear climate responses.