An intermolecular potential model of H2O with six interaction sites is proposed. The model is developed for the simulation of ice and water near the melting point. Parameters in the potential are determined to reproduce the real melting point of ice, and densities of ice and water near the melting point, which are predicted by calculating derivatives of the free energies and volumes of ice and water against potential parameters. Free energy calculations are carried out for several ice structures and water, and the results are compared with those obtained in four- and five-site models, which are currently in use. It is shown that, only in the present six-site model, the proton-disordered hexagonal ice is the stable structure at the melting point, as in real ice. The melting point of the proton-disordered hexagonal ice at 1 atm is estimated to be 271±9 K in the present model, which is in good agreement with the real melting point of 273.15 K. Moreover, results of Monte Carlo simulations of ice and water show that the present six-site model reproduces well the real structural and thermodynamic properties of ice and water near the melting point.