Abstract: A multigrid method for generating the time-dependent body fitted coordinate is given in this paper. This method can be used to generate the required time-dependent computting grids in rather short computer time. So it can be used for calculating the unsteady aerodynamics of a flexible body accuratly, especially in transonic unsteady flows.The computting grids for NACA-0012 airfoil under oscillation in pitch, as well as an elastic sine model>, are shown in the paper for demonstration.