In the present paper, the effect of fins presence on natural convection between coaxial annuli was investigated, numerically. The external duct was circular and the internal ducts included three circular, square, and triangular cross sections for discussed annuli. As a geometrical constrain, both cross section area and diameter of external duct of annuli were considered equivalent together for all investigated cases. The area of fins installed on the internal ducts was constant, and their effects on thermal behavior of annuli were compared with considering the constant wall temperature boundary condition for surfaces in the range of 105≤Ra≤108. The results showed that with increase of Rayleigh number and consequently velocity, the heat transfer coefficient was increased for both surfaces. However, presence of fins reduced the values of heat transfer coefficient of internal ducts about 50%, while they increased those values for external ducts. Also, in the case of circular annulus, with increase of Rayleigh number, the Nusselt number wincreased about 71% and 64% for non-finned and finned ones, respectively. As a result, fins increased the overall heat transfer rate of both surfaces of annuli about 13% in comparison of non-finned surfaces.