This paper presents the results from computational fluid dynamics (CFD) simulations of heat and mass transfer of pure vapor flowing and condensing in a vertical cylindrical condenser system at various inlet temperatures, mass flow rates, and operating pressure for the case where the vapor condensation is not completed inside the condenser tube. The heat and mass transfer inside the condenser tube is simulated as single phase flow, and the thin condensate film on the condensing surface is replaced by a set of boundary conditions that couple the CFD simulations inside the condenser tube and the coolant channel. The CFD results are compared with the experimental results, and good agreement has been found for the various measured temperatures. It is found that both the wall temperature and the heat flux vary significantly along the condenser tube, and it is necessary to consider the conjugate problem that consists of the whole condenser system (condenser plus coolant flow) in predicting the pure vapor condensation in a condensing system. The CFD results show that the heat flux along the condenser tube can be increasing for counter-flow condenser, and the condensate film may not be the main limiting factor in the pure vapor condensation. The results from the CFD simulations also show that the estimation of the interface shear stress cannot be based on the bulk velocity of the water vapor alone.