A numerical study is presented on double-diffusive natural convection within a vertical circular porous annulus. Flows are driven by the imposed constant temperature and concentration differences across the vertical walls of the enclosure. We use the Brinkman extended Darcy model. The flow is assumed to be laminar and two-dimensional. The density variation is taken into account by the Boussinesq approximation. The finite-volume approach is used for solving the governing equations. Solutions for the flow fields, temperature and concentration distributions and Nusselt, and Sherwood, numbers are obtained in terms of the governing parameters of the problem. The effect of both the Darcy number (Da) and the radius ratio, κ, are found to be significant. The possible existence of governing group that is valid for both a pure viscous fluid and a Darcy porous medium emerge from the present study.