The purpose of this paper is to find an optimum surface geometry of vertical condenser tubes where condensation takes place on the outer surfaces. The guiding principle on optimum condensation performance is to make the thickness of condensate liquid on the surfaces as thin as possible. A vertical tube with longitudinally parallel tiny fins is preferable because condensate is made thinner over the widest possible region. According to an analysis, there are four controlling factors for the optimum fin; sharp leading edge, gradually changing curvature of fin surface from tip to the root, wide groove between fins to collect condensate and horizontal discs attached to the tube to remove condensate. The analytical result is checked by experiments using R-113. The optimum fin shape, fin pitch and spacing of discs are found by numerical calculations for R-113 and water.