A small-system grand canonical ensemble Monte Carlo method is developed to evaluate cluster size distribution and barrier to the nucleation in a supersaturated Lennard-Jones vapor. The theoretical foundation is a physical cluster theory in which the Stillinger cluster is used as a prototypical physical cluster. Using method of Mayer's cluster expansion, the cluster-vapor interaction is effectively taken into account. From a separate canonical ensemble Monte Carlo simulation using a test particle method, the averaged volume of the cluster is obtained and is also incorporated in the small-system ensemble simulation. By this implementation our simulation is computationally more efficient compared to that based on the n/v Stillinger cluster theory in that instead of searching the saddle point on a two-dimensional free energy surface (a function of cluster size n and volume v) one needs only to find the peak on a free energy curve (a function of n only). A comparison with the height of barrier obtained from a large-system ensemble Monte Carlo simulation [K. Oh and X. C. Zeng, J. Chem. Phys. 110, 4471 (1999)] shows that omission of the vapor-cluster attraction can cause an overestimation of the height by several k(B)T.