A numerical study is made of a double diffusive stratified convection in a rotating annulus. Qualitative characteristics of the fluid flows is described with the variations of two diffusive effects, i.e., temperature and salinity gradient, where the fluid is initially rest with a pre-existing stably stratified solutal gradient. High accurate pseudospectral method is employed for integrating the axisymmetric incompressible Navier-Stokes equations with the Boussinesq fluid assumption. We are to study the xplicit effects of double diffusivity of the stratification parameter St, the buoyancy ratio $R_ρ$ and Lewis number Le at fixed $R_t=10^5$, the aspect ratio is 1. The Ekman number is small enough, the aspect ratio(=height/width) is 0(1). Contourplots of all properties, profiles of radial velocity, local Nusselt number, temperature and solute, and time dependence of velocites at fixed point are presented for easy understanding of the results. When $R_ρ$ is large, convection is strongly restricted and two cells are formed. Because of weak convective motions, temperature is propagated mainly by conduction and solute distribution is not much deformed from initial value. In two celled pattern, azimuthal velocity distribution works against layered structure. When $R_ρ$ is small, vigorous convection works against layered violent heat and mass transport. Here rotation strengthen the stable stratification effects.