This work presents a numerical investigation of the natural thermosolutal convection in a very narrow horizontal annular cylinder filled with a porous medium saturated by a binary fluid. The governing equations describing the two-dimensional steady state flow are solved by an Alternating Direction Implicit scheme (ADI). In the objective to study the effect of the buoyancy ratio, −42 ≤ N ≤ 34, on flow structure and heat and solutal transfer rates, in a cavity of radius ratio R = 1.1, a fixed Rayleigh number, Ra = 50, and Lewis number, Le = 2, values are adopted. Critical buoyancy ratio values are determined for different flow structures. The obtained results show that complex multicellular flows appear when increasing the N value respectively in the cooperating and opposite cases.