A time-independent finite difference scheme is developed and applied to analyze the viscous flow past a translating circular cylinder. In this scheme, the instantaneous moving cylinder face is mapped to a fixed boundary and the computational domain is, therefore, time independent. Large Reynolds number and high oscillating frequency of moving cylinder are used in the analysis. The finite difference approximation and algorithm were validated by the reported numerical simulation and flow visualization. The vorticity and streamline patterns developments were described and discussed. The surface vorticity distribution and position of separation point versus phases of oscillating stages were discussed. The flow behaviors of various amplitudes of exciting velocity and frequencies of moving cylinder are simulated and compared. The in-line forces on cylinder during cylinder oscillation were calculated and are in good agreement with those predicted by Morison's equation. The developed scheme can be extended to analyze the viscous flow passing an arbitrary moving cylinder.