  In this paper, a variational perturbation scheme for nonrelativistic
many-Fermion systems is generalized to a Bosonic system. By calculating the
free energy of an anharmonic oscillator model, we investigated this variational
expansion scheme for its efficiency. Using the modified Feynman rules for the
diagrams, we obtained the analytical expression of the free energy up to the
fourth order. Our numerical results at various orders are compared with the
exact and other relevant results.
