The solubility of CH4 in water + t-butyl alcohol (TEA) mixtures has been measured at 283.15, 288.15, 293.15 and 298.15 K respectively and at pressures of up to 5 MPa. The solubility varies slowly with the composition of the solvent in the water-rich region and maxima and minima are observed in solubility versus solvent concentration curves at the lower temperatures. Anomalous behaviour of the solubility observed can be explained by the existence of a clathrate-like structure, which has been suggested by other authors. The standard thermodynamic functions are also closely related to the clathrate sturcture. The shapes of the solubility isotherms at different pressures are nearly the same, which shows that the dissolved gas and pressure do not significantly affect the structure of the solvent mixtures.