We have determined the diffusion constants of oxygen molecule (D-O2) in near- and supercritical water (the SPCE model) over the wide density region by molecular dynamics simulations. Anomalous temperature dependence of D-O2 has been observed: D-O2 decreases with increasing temperature from 647 to 773 K at the 115 and 217 kg m(-3). The memory function for the friction on the diffusion shows that D-O2 is mainly dominated by the binary part of the friction, which is closely related to the contact value of the radical distribution function between oxygen and water. This value decreases with decreasing the temperature from 773 to 647 K, which is a main reason of the peculiar temperature dependence of D-O2.