There may be condensation on the fin surfaces of the air conditioning systems due to the temperature of the fin surfaces being below the dew point temperature of the water vapor in the surrounding air. Heat and mass transfer occur from the saturated air layer to the liquid water film and the latent heat of condensation is transferred to the fin. This study presents a quasilinearization solution for vertical rectangular fins when condensation occurs, assuming that the average convective heat and mass transfer coefficients are constant along the height of the fin. Rectangular fins with and without condensation on the surface have been compared and optimum fin dimensions have been given. The optimum fin length, the fin effectiveness and the average fin temperature in the case of condensation were found to be smaller than in the case of no condensation.