First-order and second-order perturbations to the energy of Gaussian beam by a doubly polarized weak gravitational plane wave in static magnetic fields are discussed.The results of numerical estimation show that the perturbation to Gaussian beams by weak gravitational plane waves is very small,i.e.the total energy of the background fields would not change obviously in the influence of gravitational waves,but the perturbative power flux produced in the local region may be observable.