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Natural convection in a concentric annulus has received considerable interest not only due to its fundamental aspects but also due to its importance in many industrial applications. These applications include electronic cable cooling systems, nuclear reactors, food processing devices and manifolds of solar energy collectors. The problem of free/natural convection in a concentric annulus filled with Micropolar fluid has been numerically investigated using Fourier spectral method. The full governing equations of momentum, angular momentum and energy have been solved to give the details of flow and thermal fields. The heat convection process in the annulus is mainly controlled by Rayleigh number Ra, Prandtl number Pr, radius ratio Rr and material parameters of Micropolar fluid. The study has considered the effect of all these controlling parameters on flow and thermal fields.