The heterogeneous nucleation of liquid droplet on a solid surface was simulated with the molecular dynamics method. Argon vapor was represented by 5760 Lennard-Jones molecules and the solid surface was represented by one layer of 1020 harmonic molecules with the constant temperature heat bath model using the phantom molecules. The potential parameter between solid molecule and vapor molecule was changed to reproduce various surface wetabilities. After the equilibrium condition at 160 К was obtained, temperature of the solid surface was suddenly set to 100 К or 80 К by the phantom molecule method. The observed nucleation rate, critical nucleus size and free energy needed for cluster formation were not much different from the prediction of the classical heterogeneous nucleation theory in case of smaller cooling rate. The difference became considerable with the increase in cooling rate and with increase in surface wettability because of the spatial temperature distribution.