This paper reports a numerical study of double-diffusive natural convection through an annular space delimited by a square cylinder on the outside and a cylindrical cylinder on the inside covered by a porous layer. The Darcy-Brinkmann-Forchheimer is used for modeling flow in both fluid and porous areas. The annular space is partially or completely filled with an isotropic porous medium. A finite volume method, using the Patankar-Spalding technique is used for solving the discretization of the dimensionless equations governing the problem. The effects of simultaneously applied thermal and solutal buoyancy forces on heat and mass transfer are shown in the results for a large range of buoyancy ratios N, Rayleigh number, and thermal conductivity. Streamlines, isotherms, and iso-concentrations are presented to analyze the flow structure transition from mass species dominated to thermal dominated flow. Results show that the buoyancy ratio can change the flow pattern and the increased thermal conductivity ratio can improve heat and mass transfer. A good agreement was obtained between the present results and those published were found.