A New type of Boundary condition for the Monte Carlo statical physics, stochastic boundary condition (SBC), has been proposed in this paper. The SBC is tested on the Lebwohl-Lasher model nematogens with 4×4×4 to 16×16×16 particles. Results for the transition temperature from nematic to isotropic and the order parameters are in good agree with those obtained from the simulation of much larger systems. Comparison with the results obtained from the conventional periodic boundary condition (PBC) shows that the SBC approaches the thermodynamic limit (N→∞) much faster than PBC. Terefore, high accuracy is achievable by using SBC with relatively small number of particles. The new boundary condition is fairly general and should be applicable in a variety of simulations.