This paper presents an improved unstructured grid immersed boundary method. The advantages of both immersed boundary method and body fitted grids which are generated by unstructured grid technology are used to enhance the computation efficiency of fluid structure interaction in complex domain. The Navier-Stokes equation was discretized spacially with collocated finite volume method and Euler implicit method in time domain. The rigid body motion was simulated by immersed boundary method in which the fluid and rigid body interface interaction was dealt with VOS (volume of solid) method. A new VOS calculation method based on graph was presented in which both immersed boundary points and cross points were collected in arbitrary order to form a graph. The method is verified with flow past oscillating cylinder.