Pre-stack inversion is a significant method for extracting lithology and fluid information from pre-stack seismic data. And the reflection coefficient approximation equation is important for pre-stack inversion. In this paper, the approximation equations of the P-wave and S-wave reflection coefficients are re-derived. The new equations consist of the fluid factor F and the lithology factor μρ. An accuracy analysis of the novel equations is carried out to verify the reliability of the proposed equations.In the process of inversion, combined with Bayesian theory, the trivariate Cauchy distribution constraint is introduced as the a priori information of the model parameters, which can stabilize the inversion results and improve their resolution. In order to obtain reliable low-frequency information, the low-frequency constraint term is constructed and added in the objective function to further improve the accuracy of the inversion results. Both the model and the field data tests show that the proposed inversion method can directly extract high-precision parameters of F and μρ from the seismic data, which provides a new calculation concept for reservoir characterization and fluid discrimination.