The interaction between a very-high-frequency gravitational wave (VHFGW) and an electromagnetic wave (EMW) in a rectangular waveguide is discussed in the weak field limit. The background EMW is assumed to be initially in the TE10 mode along the waveguide. It is then shown that a VHFGW, having the same frequency and direction of propagation of the EMW, induces through the waveguide a TE mode with a frequency doubled when compared to the original EMW frequency. In that respect, the GW acts similar to a non-linear medium, giving rise to a Second Harmonic Generation (SHG) effect. The interaction between a high-frequency gravitational wave and an electromagnetic wave in a waveguide is discussed in the linearized theory. It is shown that a gravitational wave, having the same frequency as the electromagnetic wave, gives rise to a Second Harmonic Generation effect, exciting a frequency-doubled electromagnetic mode in the waveguide. An estimate of such effect is presented.image