An accurate understanding of the thermodynamic stability of gas hydrates in salt-bearing systems is of great significance for predicting the extent of hydrate accumulation and determining the hydrate decomposition domain. Therefore, this study proposes a thermodynamic model for predicting the temperature–pressure-salt concentration three-dimensional phase-equilibrium surface. The model considered the interaction of the electrolyte in a mixed salt solution system and non-spherical shaped hydrate crystal cavity. The modified van der Waals-Platteeuw (vdW-P) model and Benedict-Webb-Rubin-Starling (BWRS) equation of state were used to describe the hydrate phase. The Pitzer-Debye-Hückel equation and nonelectrolyte non random two liquid non random factor (N-NRTL-NRF) activity coefficient model were used to describe the fluid phase. The prediction results of the model agreed with the experimental data, and the absolute average relative deviation in temperature (AARD-T) under pure water conditions was only 0.08, and the AARD-T under electrolyte conditions did not exceed 0.15, which proved the accuracy and reliability of the model. The calculation results showed that when the mole fraction of chloride salt was greater than 0.02 and the pressure was higher than 20 MPa, chemical factors caused the p-T curves to translate. When the pressure was low, the temperature gradient along the direction of the salt concentration changed drastically, and the p-T curves no longer had translation characteristics. In comparison, under the same mole fraction, AlCl3 had a stronger inhibitory effect on the CH4 hydrate than the other chloride salts. The lnp-X-1/T three-dimensional surface of the CH4 hydrate exhibited good Clausius-Clapeyron linear behavior locally, and the surface had certain nonlinear characteristics. The degree of nonlinearity of the lnp-X-1/T three-dimensional surfaces of different types of chloride salts was different. A better inhibitory effect of the chloride salt electrolyte on the CH4 hydrate was associated with stronger nonlinearity between 1/T and lnp.