Dry Steam flow at blade passages of steam turbines' low pressure stages occurs due to rapid expansion, delay in condensation and the condition of supercooled dry steam and finally after nucleation and condensation shock, phase change from vapor to liquid droplets occurs which is called two-phase or wet steam flow. In this paper, the aim of developing finite-volume flow of wet Jameson is considered for the first time in two-dimensional study by using the advantages of CUSP's numerical method. In this paper, equations governing the formation of liquid phase are combined with equations of survival and by using CUSP's numerical approach in Jameson's finite-volume method (the integrated method) the positive features of both of these methods can be simultaneously used in the modeling of two-phase flow. To calculate nucleation, the classical equation of nucleation with appropriate correction and also Lagrangian solution for growth of droplets are used in integrated method. Additionally, condensation shock effect on the pressure distribution and the droplet size has been calculated and compared with experimental data. Given the importance of areas of shocks on the suction surface of the blade, the focus of integrated method is shifted to this area. The results of integrated two-phase model are examined in subsonic and supersonic flow output .In the shock area on suction surface blade, using the CUSP's method (the integrated method) shows a better coverage in predicting attributes of flow in target area in comparison with the experimental data by a reduction of 20 percent in numerical errors.