In order to provide the foundation for immersed boundary points setting in the Immersed Boundary-Lattice Boltzmann Model (IB-LBM) frame, the numerical stability with the different Coupling Ratio of Grid (CRG) between the IB and LBM is studied. As the theoretical model to be verified for the applicable coupling ratio, flows around a circular cylinder with the Reynolds number of Re=40 and 100 are calculated, respectively. The distribution of streamline, the length of wake vortex, and the drag coefficient are analyzed for the case of Re=40 with the 4-point Piecewise Delta function being adopted in IB, the calculating results indicate that an acceptable range for CRG is 0.2-2, it is also essentially true for the case of Re=100. However, a different CRG range of 1.5—2 is found while the 4-point Cosine Delta function is used, the fact indicates that the 4-point Piecewise Delta function has a wider range for setting CRG, it is of great value to the optimal choices for Delta function and corresponding CRG in the IB applications.