A molecular simulation methodology with an algorithm usually used in equation of state calculations for phase equilibria (EOS algorithm) is applied to calculations of vapor-liquid equilibria of pure oxygen and ethane. This method can be used to determine fluid phase equilibria of pure substances and/or multicomponent mixtures by performing a single simulation, and any kinds of method to determine chemical potentials can be used. Molecular simulations of vapor-liquid equilibria for pure oxygen and ethane are performed in a very wide temperature range, from the triple points to the critical points. A two-center site-site potential model is used for oxygen and ethane, and the potential parameters are empirically determined from comparisons with experimental saturation properties. For the site-site potential function, the Lennard-Jones (LJ) potential and the Barker-Fisher-Watts (BFW) potential are used. The simulation results using the BFW potential gave better agreement with the experimental saturation properties.