This work applies the molecular dynamics simulation method to study a Lennard-Jones liquid thin film suspended in the vapor and to explore the film thickness effect on its stability. For the accurate estimation of local pressure distributions in the film, an improved method is proposed and used. Simulation results indicate that profiles of the local surface tension distribution vary widely with film thickness, while surface tension values and density profiles show little variation. As the film gets thinner, the two liquid-vapor interfacial regions begin to overlap and liquid-phase molecules in the center region of the film experience larger tension in the direction parallel to the film surface. Such interface overlapping is believed to destabilize the film and the occurrence of film rupture depends on the system temperature and the cross-sectional area of the computational domain.