Marangoni convection accompanying mass inflow from a deformable free surface, as is observed in the condenser section of a two-component heat pipe, was analyzed numerically by using a boundary-fitted coordinate system. It was shown that the condensed liquid is stable even in a gravity-free state. When the condensation rate and the Marangoni force throughout the condenser section are constant, condensate thickness distribution converges to a prescribed value regardless of the initial value, but it depends on various factors such as Marangoni number. In the case of a large Bond number, reflux of the condensed liquid by the Marangoni effect may be impossible if the gravitational force due to the difference in the heights of the liquid surfaces exceeds the Marangoni force, even if the heat pipe is horizontal. Calculated condensate thickness and velocity distribution were found to differ from the results by Nusselt's theory, but approximated to the values calculated by a simple parallel flow model as long as the Marangoni number is not very small. It was shown that the absence of Marangoni force in a part of the condenser section does not necessarily make it impossible for the working liquid to flow back, but that if the Marangoni force is absent at the edge of the condenser section, the value of the contact angle between the liquid and the inner wall has a significant effect on the condensation thickness distribution.