Equilibrium molecular dynamics simulations were carried out to study the diffusion process of oxygen in supercritical water (SCW). Both infinite-dilution diffusion and Maxwell-Stefan (MS) mutual diffusion coefficients were calculated. The differences between the simulated Maxwell-Stefan diffusion coefficients and those predicted by the Darken equation were examined. It suggests that the velocity cross correlation function plays an important role in the oxygen-SCW mutual diffusion. The Darken equation may not be valid in predicting the Maxwell-Stefan diffusion coefficients for this mixture.