The free energy of homogeneous nucleation is estimated by the Monte Carlo simulations on the supersaturated Lennard-Jones (U) vapor phase. The calculation is performed on the each system with a fixed number of particles N (1 < N < 109). The periodic boundary condition is assumed. The volume per a particle is 43.2 in units of LJ system. No carrier gas particles are included. The range of temperature is from 0.01 to 1.00 in units of Lennerd-Jones system. The initial configuration is distorted cubic lattice, and the sample is cooled to low temperature, where all molecules become a large cluster. In the second stage, it is heated to vaporize, where the monomer phase is obtained. In the third run, the low,temperature sample is heated with a condition that the cluster is not allowed to decompose in the Monte Carlo (MC) simulations. The free energies of the cluster phase and the monomer one are obtained by the thermodynamic integration. The obtained critical size is about 30-40 at temperature 0.67 in units of U system, which is comparable to the molecular dynamics (MD) simulation with the carrier gas particles.