Hydrate phase equilibrium data on mixed ternary gas systems, including low-concentration hydrogen sulfide in the presence of inhibitors, are very limited in the literature. In this study, we experimentally investigated the effect of combined monoethylene glycol and brine (containing sodium chloride or calcium chloride salts) on inhibiting ternary sour gas hydrate (CH4 + C3H8 + H2S) formation. The hydrate formation experiments were performed in the temperature and pressure ranges of 276.75–296.05 K and 2.29–12.08 MPa, respectively, using the isochoric method with stepwise heating. In addition, a comparison between the experimental data and commercial software (HydraFlash) was performed. Furthermore, the experimental results were compared with the published data of the same ternary systems (without inhibitors) to show the impact of low-concentration hydrogen sulfide on hydrate formation. The results indicated that the presence of various inhibitors in the system led to a change in the equilibrium curve of the ternary sour hydrate to the left side of the equilibrium curve, indicating the thermodynamic inhibition effect. Also, the hydrate inhibition performance of our mixed aqueous inhibitor systems can be summarized as follows: (20 wt % MEG + 10 wt % NaCl) > (20 wt % MEG + 6 wt % CaCl2 + 4 wt % NaCl) > (20 wt % MEG + 10 wt % CaCl2) > (20 wt % MEG) > (DW). Moreover, decreasing the hydrogen sulfide concentration to the 0.01 mole fraction in the feed gas leads to a shift in the sour gas hydrate equilibrium curve to areas with lower temperatures and higher pressures. Finally, the experimental data obtained for all systems with an average total absolute deviation% of 0.12 had an acceptable agreement with the prediction of HydraFlash software.