Cloud droplet size distributions (CDSDs), which are related to cloud albedo and rain formation, are usually broader in warm clouds than predicted from adiabatic parcel calculations. We investigate a mechanism for the CDSD broadening using a moving-size-grid cloud parcel model that considers the condensational growth of cloud droplets formed on polydisperse, submicrometer aerosols in an adiabatic cloud parcel that undergoes vertical oscillations, such as those due to cloud circulations or turbulence. Results show that the CDSD can be broadened during condensational growth as a result of Ostwald ripening amplified by droplet deactivation and reactivation, which is consistent with early work. The relative roles of the solute effect, curvature effect, deactivation and reactivation on CDSD broadening are investigated. Deactivation of smaller cloud droplets, which is due to the combination of curvature and solute effects in the downdraft region, enhances the growth of larger cloud droplets and thus contributes particles to the larger size end of the CDSD. Droplet reactivation, which occurs in the updraft region, contributes particles to the smaller size end of the CDSD. In addition, we find that growth of the largest cloud droplets strongly depends on the residence time of cloud droplet in the cloud rather than the magnitude of local variability in the supersaturation fluctuation. This is because the environmental saturation ratio is strongly buffered by numerous smaller cloud droplets. Two necessary conditions for this CDSD broadening, which generally occur in the atmosphere, are as follows: (1) droplets form on aerosols of different sizes, and (2) the cloud parcel experiences upwards and downwards motions. Therefore we expect that this mechanism for CDSD broadening is possible in real clouds. Our results also suggest it is important to consider both curvature and solute effects before and after cloud droplet activation in a cloud model. The importance of this mechanism compared with other mechanisms on cloud properties should be investigated through in situ measurements and 3-D dynamic models.