The prediction of in-situ stress is a critical parameter for guiding reservoir hydraulic fracturing, which influences the size, orientation, and morphology of reservoir fractures. Hydraulic fracturing of reservoirs is beneficial for the storage and transportation of oil and gas, and is of great significance for increasing oil and gas production. This paper proposes a method for predicting in-situ stress in HTI media based on Bayesian inversion. Firstly, considering the abundant vertical fractures in tight sandstone reservoirs, these are equivalent to HTI media. Based on the theory of HTI media anisotropy and Bayesian inversion, elastic parameters and anisotropy parameters of the underground media are obtained through pre-stack seismic data. Subsequently, the prediction of in-situ stress is achieved by utilizing the inverted elastic parameters and anisotropic parameters based on the principal stress calculation equation for HTI media. Finally, the Differential Horizontal Stress Ratio (DHSR) distribution is used to indicate areas in the reservoir that are easily amenable to fracturing and rich in oil and gas resources. Model data testing verifies the feasibility and noise resistance of the inversion algorithm, and application results from actual data demonstrate that the DHSR obtained from pre-stack seismic data inversion can effectively indicate areas in tight sandstone reservoirs that are easily fracturable, holding important implications for breakthroughs in the efficiency of tight sandstone oil and gas reservoir exploitation.