In this paper, new experimental measurements of methane (CH4) solubility in the ionic liquid (IL) 1-hexyl-3-methylimidazolium tricyanomethanide ([hmim][TCM]) are presented. The solubility data were obtained using a synthetic method based on bubble-point pressure measurements for concentrations ranging from (2–10) CH4 mole% and within a temperature range of (293–363 K) and pressures up to 10 MPa. The results obtained in this work were compared with those obtained for other ILs. The IL [hmim][TCM] was found to show the lowest CH4 solubility, which is desired for application of this IL as gas sweetening solvent (low co-absorption of hydrocarbons). Moreover, the CH4 solubility was compared to the CO2 solubility in the same IL, showing that [hmim][TCM] can selectively absorb CO2 from natural gas. The experimental solubility data of CH4 in [hmim][TCM] were accurately modeled using the PR-EoS with only one temperature-independent binary interaction parameter.