The paper deals with the optimization of the convective annular fins with consideration of the base wall thermal resistance. In practice, the surface temperature at the fin base is usually unknown. The general solution for annular fins of arbitrary profiles with the thermal resistance boundary is obtained analytically in terms of Bessel function. Consequently, the optimum heat transfer rate from the fin and the optimum fin dimensions are computed. The numerical results of the optimum design charts are presented in terms of fin characteristic number, profile number, and overall wall thermal resistance.