Pool boiling and in-tube condensation phenomena have been investigated intensively during the past decades, due to the superior heat transfer capacity of the phase change process. In passive heat removal heat exchangers of nuclear power plants, the two phase-change phenomena usually occur simultaneously on both sides of the tube wall to achieve the maximum heat transfer efficiency. However, the studies on the effects of in-tube condensation on external pool boiling heat transfer are very limited, especially in numerical computation aspect. In the present study, the saturated pooling boiling over a vertical tube under the influences of in-tube steam condensation is investigated numerically. The Volume of Fluid (VOF) interface tracking method is employed based on the 2D axisymmetric Euler-Euler multiphase frame. The phase change model combining with a mathematical smoothing algorithm and a temporal relaxation procedure has been implemented into CFD platform by user defined functions (UDFs). The two-phase flow pattern and bubble behavior have been analyzed. The effects of inlet steam mass flow rate on boiling heat transfer are discussed.