A fully conservative zonal interface algorithm for overlapped (Chimera) grid has been extended to handle moving body flows. To ensure flow conservation, the motion of the computational grid needs to be taken into account. Several new issues arising from moving and deforming grids, e.g., vanishing and new-born cell problems, are addressed with a cell-merging-unmerging technique. The grid velocities are determined in a way which satisfies free-stream preserving (the Geometric Conservation Laws)The flow solver is based on a fully implicit, cell-centered finite volume discretization with MUSCL reconstruction and Roe's approximate Riemann solver. The interface algorithm is first validated by tackling the case of supersonic flow over a cylinder. Then several moving body flow problems are simulated using the current approach to demonstrate its capabilities.