Most of the theoretical models of pure vapor condensation for annular two-phase flow in a vertical tube so far assume that the vapor stream is fully developed already at the tube inlet. In this study, laminar film condensation of pure vapor flow in a vertical tube is addressed within the framework of the boundary-layer theory. Here, we take into account (i) the vapor flow rate reduction owing to condensation, (ii) the finiteness of the vapor boundary layer thickness, (iii) the curvature of the vapor layer, and (iv) the pressure variation. An approximate integral two-phase boundary layer equation model is derived, without relying on any empirical correlation for the vapor friction. Furthermore, the present model can be further simplified to obtain an analytical solution if the degree of subcooling is sufficiently large. From the numerical analysis of the model, the condensate film thickness, the average Nusselt number and the pressure variation are shown as a function of the distance from the tube inlet or the tube length. The asymptotic solution for sufficiently large degrees of subcooling gives a good approximation to the numerical solution. The tube length of complete condensation is estimated. Comparison with vertical plane condensation demonstrates that the film thickness and the Nusselt number increased and decreased, respectively, by the vapor flow reduction for large degrees of subcooling.