We performed a molecular dynamics simulation of the boiling nucleation process of liquid argon faced on heated solid surface. The solid wall at the bottom of calculational domain consisted of platinum molecules based on a harmonic potential and the interaction between argon and platinum particles was calculated by Lennard-Jones potential function. The periodic-shell boundary condition was employed at the upper boundary of domain as a simulant of liquid argon pool. The simulation started from equilibrium condition at 100 K. The temperature of argon increased with increase in that of wall molecules. It was confirmed that the boiling occurred and the vapor bubble developed near heated solid wall with an increase in heated time.