A Cartesian grid based on Immersed Boundary Method(IBM),proposed by the present authors,is extended to unstructured grids.The advantages of IBM and Body Fitted Grid(BFG)are taken to enhance the computation efficiency of the fluid structure interaction in a complex domain.There are many methods to generate the BFG,among which the unstructured grid method is the most popular.The concept of Volume Of Solid(VOS)is used to deal with the multi rigid body and fluid interaction.Each body surface is represented by a set of points which can be traced in an anti-clockwise order with the solid area on the left side of surface.An efficient Lagrange point tracking algorithm on the fixed grid is applied to search the moving boundary grid points.This method is verified by low Reynolds number flows in the range from Re =100 to 1 000 in the cavity with a moving lid.The results are in a good agreement with experimental data in literature.Finally,the flow past two moving cylinders is simulated to test the capability of the method.