This study discusses how the sensitivity of climate may be affected by the variation of cloud cover based on the results from numerical experiments with a highly simplified, three-dimensional model of the atmospheric general circulation. The model explicitly computes the heat transport by large-scale atmospheric disturbances. It contains the following simplifications: a limited computational domain, an idealized geography, no heat transport by ocean currents and no seasonal variation. Two versions of the model are constructed. The first version includes prognostic schemes of cloud cover and its radiative influences, and the second version uses a prescribed distribution of cloud cover for the computation of radiative transfer. Two sets of equilibrium climates are obtained from the long-term integrations of both versions of the model for several values of the solar constant. Based on the comparison between the variable and the fixed cloud experiments, the influences of cloud cover variation on the response of a model climate to an increase of the solar constant are identified. It is found that, in response to an increase of the solar constant, cloudiness diminishes in the upper and middle troposphere at most latitudes and increases near the earth's surface and the lower stratosphere of the model particularly in higher latitudes. Because of the changes described above, the total cloud amount diminishes in the region equatorward of 50° latitude with the exception of a narrow sub-tropical belt. However, it increases in the region poleward of this latitude. In both regions, the area mean change in the net incoming solar radiation, which is attributable to the cloud-cover change described above, is approximately compensated by the corresponding change in the outgoing terrestrial radiation at the top of the model atmosphere. For example, equatorward of 50° latitude, the reduction of both cloud amount and effective cloud-top height contributes to the increase in the area-mean flux of outgoing terrestrial radiation and compensates for the increase in the flux of net incoming solar radiation caused by the reduction of cloud amount. Poleward of 50° latitude, the increase of cloudiness contributes to the reduction of both net incoming solar and outgoing terrestrial fluxes at the top of the model atmosphere. Although the effective cloud-top height does not change as it does in lower latitudes, the changes of these fluxes approximately compensate each other because of the smallness of insolation in high latitudes. Owing to the compensations mentioned above, the changes of cloud cover have a relatively minor effect on the sensitivity of the area-mean climate of the model.