The study of water waves in ocean regions and their coastlines, without considering the wave-current interaction effects is incorrect. In this paper, the wave-current interaction is investigated. Winds, explosions, ship motions and earthquakes are the main causes of water waves in the oceans. In the coastal zones, water waves interact with long shore currents.Analytical, numerical and experimental models are available for solution of the wave-current interaction problems. The numerical solution of the governing equations; is carried out in two phases, Viz. a 'wave phase' and a "current phase'. In the wave level calculation, the current field is known and the wave ray paths are determined through step by step integration of a set of differential equations. In each step of integration, the equation of the wave action conservation and wave number conservation are solved to determine wave height and wave number, respectively. In the current phase, the characteristics of waves are known, and the governing equations of the shallow water are solved by Galerkin finite element method and the current unknowns (velocity and depth) are determined. The calculations are initiated in a wave phase, where currents are neglected. The two-level iterative model is continued until the results are converged.Based on this method, two computer programs called "SWERM" and "CAFEM" are developed in FORTRAN 77. Several examples are studied and the results are presented.The results showed that, when the current has a positive component in the direction of wave propagation, the wave lenght increases and the wave height decreases. Conversely, a negative current component reduces the wave lenght and increases the wave height.Also, for current in the direction of wave, current velocity increases. The results are compared with cited results, and the accuray of results are checked.