In a recent paper we predicted the fluid-phase equilibria of n-butane + n-alkane binary mixtures using the statistical associating fluid theory for chain molecules with attractive potentials of variable range (SAFT-VR). Now we focus on the methane + n-hexane system, again using the SAFT-VR approach. The methane + n-hexane system exhibits type V phase behavior, in which partial miscibility of the two components is observed. The phase diagram for the binary mixture is predicted, and we concentrate on the critical region and liquid-liquid immiscibility observed in this system. The upper and lower critical end-points predicted by the SAFT-VR approach are in excellent agreement with the experimental data, as is the theoretical gas-liquid critical line. We treat the n-alkane molecules as chains of united-atom hard-sphere segments with square-well potentials of variable range to describe the attractive interactions. A simple empirical relationship exists between the number of carbon atoms in the alkane molecule and the number of segments in the chain model. The pure component vapor pressure curves and saturated liquid densities are calculated by fitting to experimental data from the triple to the critical point. The optimized parameters are then rescaled to the respective critical points. We use the Lorentz-Berthelot combining rules for the unlike size and energy interactions. It is particularly gratifying to see that type V behavior can be predicted for the methane + n-hexane system simply by using Lorentz-Berthelot combining rules.