The growth by steam condensation of an hygroscopic aerosol is investigated using the condensation rate model which has been derived from the mass and heat transfer equations. The present model accounts for both the solute and Kelvin effects. When the hygroscopicity is considered, condensation can occur on hygroscopic seed particles even under subsaturated steam conditions. This study focuses on the effect of hygroscopicity on the evolution of the particle size distribution and decay of the total aerosol concentration. It is found that hygroscopicity causes the particle size distribution to rapidly move upward even in a very short time, resulting in substantially higher decay of the total aerosol concentration than the case without considering hygroscopicity.