We report Monte Carlo (MC) simulations of the Lennard-Jones (LJ) fluid at the liquid-vapor interface in the critical region. A slab-based tail method is associated with the MC simulations to approach as close as possible the critical point (T* = 0.98T*(C) thorn. We investigate then the impact of system-sizes on the surface tension and coexisting densities by considering very large box dimensions for which the surface tension is independent of system-sizes at low temperatures. (C) 2018 Elsevier B.V. All rights reserved.