Natural gas is gaseous fossil fuel consisting primarily of methane (CH4). Argon (Ar) is a precious gas resource among the nonhydrocarbons in natural gas, and it can be separated from the natural gas; thus, it is very necessary to understand the vapor liquid equilibrium (VLE) of (Ar + CH4). The investigations on the VLE data of (Ar + CH4) have mostly focused on the temperature range of (>140 K), while studies are relatively scarce below 140 K. In this work, the VLE data of (Ar + CH4) from 95 to 135 K were measured by experiment. Four different mixing rules (HV, MHV1, MHV2, and LCVM) with the same equation of state (PR) and the four equations of state (SRK, PR, PRSV, NM) with the same mixing rule (MHV1) were used to correlate the VLE of (Ar + CH4), respectively. The research results were discussed in detail. In addition, the excess Gibbs free energy of (Ar + CH4) was further analyzed. The results showed that the excess Gibbs free energy of (Ar + CH4) was more than zero, and the curves of excess Gibbs free energy and excess enthalpy of (Ar + CH4) had good symmetry.