As steam condensation is increasingly applied in many industrial fields, while its condensing mechanism is still unclear, the tube wall is usually set to be isothermal in numerical studies for simplification, leading to many unreasonable results. Consequently, the influence of the wall temperature distribution on vapor condensation inside tubes and the condensation mechanism were numerically studied. The governing differential equations for mass, momentum and energy are derived based on partial Nusselt thin film assumptions. The shear-force on the interface of the two phases was considered, and the wall boundary conditions were carefully selected and compared. At an isothermal wall condition, it is found that the set of wall temperature has a great impact on the condensation inside a tube. For instance, a 1K deviation of wall temperature will bring a 2% - 3% error to the average condensation heat transfer coefficient (HTC). In order to avoid the error resulted from the isothermal assumption of the wall and improve the reliability and applicability, a mathematical method based on a shell and tube boundary conditions is established. Compared with isothermal wall assumption, the errors of the heat load and the average HTC were decreased by 67.05% and 69.68% respectively. What's more important, both the wall temperature distribution and the heat load distribution are nonlinear. A large proportion of the steam is condensed in the inlet-region of a condenser, where the wall temperature changes greatly. The new model was validated by some published data form experimental study.