Sour natural gas containing high percentage of hydrogen sulfide (H₂S) often experiences severe gas hydrate blockages. Accurate prediction of hydrate formation conditions is essential for flow assurance, yet reliable highpressure data and robust models for H₂S/CH₄ hydrates, particularly those containing thermodynamic inhibitors, are limited. This study employed the single-crystal phase boundary method to determine the three-phase equilibrium conditions (H-Lw-V) of H₂S/CH₄ mixed hydrates in pure water and with inhibitors (NaCl, KCl, CaCl₂, MgCl₂, methanol, and ethylene glycol) at pressures of up to 30 MPa. Raman spectroscopy revealed that the H₂S/ CH₄ mixture forms structure I hydrate, with the H₂S and CH₄ molecules occupying both large and small cages, and their Raman peaks shifting to higher wavenumbers with increasing temperature. We developed and validated a thermodynamic model integrating the PRSV equation of state for the vapor phase, the Chen-Guo model for the hydrate phase, and the Pitzer/UNIQUAC models for the aqueous phase. This model accurately predicted equilibrium pressures for pure water, methanol, KCl, and MgCl₂ solutions, with an absolute average relative deviation of less than 10%. However, it systematically underestimated pressures for NaCl, high-concentration ethylene glycol, and CaCl₂, revealing limitations in aqueous activity predictions. Assessment of inhibitor performance and economic feasibility indicated that methanol provides effective and economical inhibition for sour gas transport at similar to 10 MPa. This study provides essential high-pressure data and Raman spectroscopic insights and establishes a reliable thermodynamic modeling framework for H₂S/CH₄ hydrates, supporting flow assurance management, inhibitor selection, and model optimization.