The NpT + test particle method for the calculation of vapour-liquid phase equilibria by molecular simulation is extended to binary mixtures. The independent thermodynamic variables are the temperature T and the liquid concentration x. On the liquid side, one NpT simulation is performed at a prescribed pressure which determines the chemical potentials and their derivatives with respect to the pressure, i.e., the partial molar volumes. On the vapour side, two NpT simulations are performed at two different concentrations and at a prescribed pressure yielding again the chemical potentials and their derivatives with respect to the pressure. Using first-order Taylor expansions for the chemical potentials, the vapour-liquid phase equilibria are obtained. As an example, the vapour-liquid phase equilibria for the mixture argon + methane are predicted at four temperatures and compared with experimental results. For that purpose, an optimized redetermination of the molecular parameters was made using only excess volumes and enthalpies for the unlike interaction.