A dynamic overset mixed grids algorithm is proposed. An interpolation method based on the linear reconstruction is developed for the overset mixedgrids approach. The optimized intergrid-boundary definition method is shown to be excellent and reliable. The intergrid boundaries are very smooth and have similar cell sizes.The flows around multiple bodies in relative motion can be simulated by solving the unsteady Navier-Stokes equations and the 6DOF equations. The numerical results of store separation prove that the present dynamic overset grids method is fast, accurate and reliable.