A three-dimensional heat-transfer analysis procedure for the coupled condensing/evaporating films flowing down along the outer/inner walls of a vertical grooved tube has been developed. It is quite complex as many important solution elements such as the free-surface tracking, the conjugate heat transfer, and the phase change, need to be carefully incorporated. To effectively treat the condensing flow along the grooved outer wall, where the free-surface location is yet to be determined, a general nonorthogonal moving grid technique is employed. Given the vapor properties on both sides, the fully elliptic Navier-Stokes and energy equations are solved for the temperature and velocity fields by using a SIMPLE-type finite volume method. The analysis is successful in capturing the free-surface location along with the amount of condensate and other major three-dimensional characteristics. Most of the condensation is seen to take place on the bare portion of the groove surface and that clearly demonstrates how the heat transfer is enhanced by the grooved surface. The results are presented for various groove densities and operating conditions. The optimum groove number appears to vary with the temperature difference of the two sides. The effect of the surface tension is also discussed.