Monte Carlo simulations for diatomic molecules were performed by using a site-site pair potential model together with a triplet potential. To reduce the computer time, an effective triplet potential is proposed. This potential expresses the effects of Axilrod-Teller three-body interactions on a pair of atoms, and is given as a simple function of density and the distance between the pair of atoms. The computer time for Monte Carlo simulations is almost equivalent to that of fluids with only the site-site pair potential. From comparisons of the Monte Carlo simulations and the experimental data of oxygen, the potential parameters are determined.