We examined the sensitivity of the formation of moist convection to the number of aerosols that serve as cloud condensation nuclei (CCN) based on a set of numerical experiments using a nonhydrostatic model with a bin cloud microphysics model. Additionally, a linear stability analysis for an air parcel incorporating effects of the CCN number concentration (NCCN) has been conducted to further demonstrate the findings in numerical experiments. The results of the numerical experiments show that moist convection does not form when NCCN ≤ 10 cm−3. The sensitivity to NCCN can be divided into three regimes: when NCCN ≤ 10 cm−3, convection does not form or not fully develop; when 1 ≤ NCCN ≤ 102 cm−3, maximum vertical velocity increases with NCCN; and when NCCN ≥ 102 cm−3, the intensity of convection does not largely depend on NCCN. We demonstrate that the main reason convection does not form under environments with a small NCCN is that the time scale for condensation is longer than that to change environmental conditions. Given a supersaturated environment, fewer droplets form when NCCN is small and the size of droplets is potentially large. Consequently, the amount of latent heating is limited and the air parcel cannot obtain buoyancy within a reasonable time scale. Linear stability analysis using a parcel model considering the effect of NCCN without ice-phase processes shows unstable and stable regimes as a function of the number of droplets. The analytically obtained critical droplet number for the convection formation well corresponds to the minimum NCCN beyond which convection forms in the present numerical experiments.