A nonequilibrium molecular dynamics(NEMD) simulation method is developed and applied to study shock waves propagating through argon gas. In this simulation method, shock waves are generated by pushing a piston at a constant speed from one side of a simulation box filled with argon molecules. A linear relationship between piston speeds and shock speeds is observed. Thermodynamic properties including density, temperature, and pressure before and after the shock front are obtained from the simulations and compared with the well-known Rankine-Hugoniot equations based on ideal gases. The comparison shows an excellent agreement, indicating that this NEMD simulation method can be employed to investigate various physical properties of shock waves further.