In order to study the contribution of the electron-phonon interaction to the Stoner susceptibility, we obtain the spin susceptibility for the Hubbard Hamiltonian system with an electron-phonon interaction. We employ the equation of motion method of the Green's function to calculate the spin susceptibility. It is found that effects of the electron-phonon interaction on the susceptibility become substantial depending on underlying electronic structures and the value of the electron-electron correlation interaction. It is also found that the phonon contribution gives rise to a linear temperature dependence of the susceptibility and a reduced Curie temperature, resolving the shortcomings of Stoner's mean field theory.