This paper describes a Cartesian grid method with cut cells for the calculation of incompressible viscous flows with moving physical boundaries. In this method, no cell merging technique is required in the conventional sense. Only pressure component on small cut cells is calculated directly. The code is developed based on Fractional Step Method on Finite Volume Method. In time integration, the second order explicit Adams-Bashforth method is used for the convective terms and second order implicit Crank-Nicholson method is used for the diffusive terms. Moving boundaries are accommodated by up-dating the local cut cell information on a stationary background mesh as the boundaries move. The code is tested on an oscillating circle cylinder and compared with other previous numerical results.