In this study, natural convection heat transfer from an annular fin on a horizontal cylinder was numerically investigated. The aim of the study was to determine the effects of geometric parameters like: fin diameter, fin spacing and base-to-ambient temperature difference on the heat transfer performance of fin arrays, and to find optimum parameters that maximize the heat transfer rate. Keeping the fin thickness at 1 ram, fin diameter was varied from 35 mm to 160 mm and fin spacing 3.5 mm to 146 mm. Surface of the cylinder as well as the surface of each fin were assumed to be at a uniform temperature. Air was selected as the working fluid. The problem was a three-dimensional natural convection phenomenon with open boundaries and was solved with a cylindrical coordinate system. The equations of mass, momentum and energy were solved using appropriate boundary conditions by means of PHOENICS. The obtained results have shown that the convection heat transfer from the fins depends on fin diameter, fin spacing and base to ambient temperature difference. Finally, a correlation was obtained for the optimum fin spacing depending on Rayleigh number and fin diameter.