A numerical study is made of a double diffusive stratified spin-up in a cylinderical cavity with an insulating side wall. The aim is to describe the unsteady flow fields characteristics qualitatively when the density field is stratified by two diffusive effects, i.e., temperature and salinity gradients. The temperature and salinity gradients make cooperating contributions to the overall density field, the undisturbed stratification of which is gravitationally stable. The Prandtl number, Pr, is set to 1 and the aspect ratio, R/H, fixed to 1. The effective stratification is seen to increase as the buoyancy ratio, R_ρ, increases, though the overall stratification parameter, St, is constant. The effective stratification becomes strong as the Lewis number increases. And the thickness of the side wall boundry layer decreases with the Lewis number. The effect of stratification becomes weak when the Ekman number is relatively large.