An implicit finite volume algorithm has been written to solve the steady one-dimensional vapor-liquid, two-phase, inviscid, compressible flow. The speed of sound definition based on flow quality and void fraction has been given along with some two-phase gas dynamic relations. Shocks have been captured by the steady Euler solver incorporating an artificial two-phase compressibility expression which has been added at transonic region according to the upwinded density concept. The fully coupled linearized system of equations is solved by a rapid Newton-Raphson solution procedure, Subcooled nitrogen flow through two convergent divergent nozzles has been analyzed. Homogeneous equilibrium and non-equilibrium results have been compared with analytical, experimental and numerical results, as means to validate the present solution.