To better application of the Cubic-Plus-Association equation of state (CPA-EoS) and van der Waals Platteeuw (vdW-P) model to the phase equilibrium modeling of the methane-rich sour natural gas, an improved CPA-EoS (iCAP-EoS) with new correlations was proposed. In terms with the new energy parameter a, the saturated liquid density of pure component would be described accurately, Additionally, instead of the constant binary interaction parameter, a temperature-dependent binary interaction parameter was developed for calculating the corresponding binary system. As the results shown, the compositions of the fluid phase for the binary mixtures could be performed accurately with the help of the temperature-dependent binary interaction parameter. The predicted results of the proposed model, for both ternary systems and quaternary systems, were compared with the experimental data on the gas hydrate equilibrium dissociation pressures in good agreements with an AAD approximately to 2.28%. Additionally the results shown that the iCPA-vdWP model had an superior accuracy than the original CPA-EoS and vdW-P(CPA-vdWP) model. In high-acidic gas system, the presented model is also within the acceptable errors. Besides the potential application for phase equilibrium model in sour-gas hydrate based separation process is also obtained. (C) 2015 Elsevier B.V. All rights reserved.