Based on the cell-centered finite volume methods (FVM), an improved unstructured overset grids interpolation method is proposed. The main improvement is to control the condition number of interpolation matrix by adjusting the radius of Wendland’s C2 radial basis function. Furthermore, the numerical singularity in the overset boundary region of radial basis function interpolation is eliminated. Using known analytic functions as interpolation samples, the accuracy of four interpolation methods, namely linear interpolation(LINE), weighted interpolation by reciprocal distance (WA), inverse quadratic radial basis function interpolation(IQ), Wendland’s C2 radial basis function interpolation(C2) were investigated. The inverse quadratic radial basis function IQ and C2 radial basis function with high accuracy were selected for further study. Then the transonic flow field of RAE2822 supercritical airfoil was simulated by using the above two radial basis functions. It is found that the flow field in the overset region of C2 radial basis function interpolation is smoother, the convergence rate is faster and the interpolation accuracy is higher. Through the numerical simulation of MD30P/30N multi-segment airfoil flow field, the effectiveness of conditional number control interpolation method in eliminating interpolation oddness is verified. Finally, the equations of six degrees of freedom rigid body are coupled, and the typical model of AEDC plug-in separation model is calculated and analyzed under the condition of transonic velocity. The accuracy and robustness of the developed conditional number control radial basis function interpolation method are further verified.