A newly proposed hybrid Cartesian-body fitted grid (HCBFG) technique is used for flow-structural interactions with large structure deformation. Based on a Cartesian background grid, the new approach automatically searches a near wall boundary(NWB) at any instant when a geometry is given. Within the NWB, a body-fitted mesh is generated using an efficient algebraic method with the skew angle between any two mesh lines guaranteed between 45° and 135°. This is attributed to the fact that only the mesh lines tangential to the solid surface needs to be generated. The mesh lines in the other two directions are from the background Cartesian grid. Outside of the NWB, the Cartesian grid is used. On the NWB, the grid points are one-to-one connected with the Cartesian grid. Hence, a consistent discretization scheme for structured grid can be used with no interpolation needed at the NWB. The fully conservative flux calculation can be achieved. With such grid system, all computation can be done on a fixed square grid in the computational domain regardless of the boundary shape and grid movement in the physical domain. Incorporated with existing capabilities of fully-coupled flow-structure interaction, this method can greatly enhance our geometric flexibility and computational capability. This new approach has the advantages of the Chimera grid and Cartesian grid methods to treat complex or moving geometry but overcomes the drawbacks of those methods requiring interpolation on the different mesh boundaries. Benefited from the HCBFG, all the rigorous numerical techniques developed for body-fitted grid, which are essential to achieve high order accuracy can be used. The mesh size of the proposed hybrid grid approach will also be substantially smaller than that of a Cartesian grid method or unstructured grids since a highly stretched grid can be used near walls. This new approach may open a door to a new class of CFD technique for efficiently and accurately simulating steady and unsteady flows, furthermore, solving moving grid and fluid-structural interaction problems with complex geometries. The study cases presented include a steady state transonic RAE2822 airfoil and a vortex-induced oscillating cylinder. The details regarding the mesh deformation and moving mesh, geometric conservation law, and fluid-structural coupling procedure are described.