Fermi resonance (FR) plays an important role in the spectral line identification and assignment in spectral analysis. It contains a wealth of physical laws which are urgently needed for research. In the present paper, we propose a new method of varying the refractive index of the solution to study the FR, which is based on the model of Onsager. The basic principle of this method is to use Raman scattering intensity (Raman scattering coefficient) changing with the refractive index of solution to study the FR. With this method we not only can give the relationship between the FR parameters and the refractive index of solution, but also find new spectrum phenomena (including the asymmetric shift of Fermi doublet and the FR tuned fundamental freguency of the overtone). In this article we provide a new research method to study the FR.