This study numerically investigates dry and moist convection forced by an urban heat island using a two-dimensional, nonhydrostatic, compressible model with explicit cloud microphysical processes (Advanced Regional Prediction System). The urban heat island is represented by specified heating. Extensive numerical experiments with various heating amplitudes, representing the intensity of the urban heat island, uniform basic-state wind speeds, and basic-state relative humidities, are performed to examine their roles in characterizing urban-induced convection. Two flow regimes can be identified in dry simulations. One regime is characterized only by stationary gravity waves near the heating region and is revealed when the urban heat island intensity is very weak. The other regime is characterized both by stationary gravity waves near the heating region and by a downwind updraft cell that moves in the downstream direction. The intensity of the downwind updraft cell increases as the heat island intensity increases or the basic-state wind speed decrease. Results of moist simulations demonstrate that the downwind updraft cell induced by the urban heat island can initiate moist convection and result in surface precipitation in the downstream region when the basic-state thermodynamic conditions are favorable. As the urban heat island intensity increases, the time required for the first cloud water (or rainwater) formation decreases and its horizontal location is closer to the heating center. It is shown that for the same basic-state wind speed and heat island intensity a stronger dynamic forcing--that is, a stronger downwind updraft--is needed to trigger moist convection in less favorable basic-state thermodynamic conditions.