The lithology and hardness of the coal seam roof are directly related to the stability and water permeability of the roadway and the safe production of the coal mine. It has become a common method to predict gas content based on AVO inversion, but the conventional AVO inversion formula is a simplified approximation of Zoeppritz equation in different degrees under certain conditions, which affects the inversion accuracy to some extent. On the basis of petrophysical analysis of the roof, the pre-stack inversion of quasi-linear Zoeppritz equation with the smallest overall angle error was employed to lithology and hardness prediction of coal seam roof in Yangquan Mining Area, Shanxi Province. The results show that the expression of quasi-linear Zoeppritz equation is simple, and through the AVO characteristic analysis of different Zoeppritz approximate formulas, found that the precision of quasi-linear Zoeppritz equation is the highest, second only to that of accurate Zoeppritz equation. The analysis of rock mechanics characteristics shows that Young’s modulus multiplied by density is the most sensitive to hardness, and pseudo-gamma P-wave velocity can effectively reflect roof lithology. The lithology and hardness characterization parameters obtained from inversion are combined with the parameter well data and geological data to comprehensively evaluate the roof stability, provide geological evidence for roadway excavation and reduce the coal mine production risk.