A method of calculating the excess Helmholtz free energy from the average of the bent effective acceptance ratio for two-center-Lennard-Jones liquids has been presented. The bent effective acceptance ratio has been newly composed from the acceptan ce ratio for the potential energy difference between a configuration in the Metropolis Monte Carlo procedure and random virtual configuration generated by the separate parallel Monte Carlo procedure and the Boltzmann factor for half the potential energy difference. The excess Helmholtz free energy was calculated directly from the average of the bent effective acceptance ratio through a single Metropolis Monte Carlo run. Because the separate parallel Monte Carlo procedure was used, this method can be applied to molecular dynamics simulations. For two-center-Lennard-Jones liquids, the average of the bent effective acceptance ratio gave better results than use of the modified effective acceptance ratio in the previous work.