An electrically controlled broadband grating based on periodically poled LiNbO3 is reported. According to the wave- coupling theory, the analytical expression of the diffraction intensity for the grating is derived, and the numerical results show that the diffraction spectrum of the grating can be tuned by an applied electric field. For example, with an applied voltage of 310 V, the diffraction efficiency of first order spectrum is greater than 60% over the band from 1.21 mm to 1.83 mm. Especially at the wavelength of 1.5 mm, it reaches 70%. With an applied voltage of 165 V, the diffraction efficiency of first order spectrum is more than 60% over the band from 0.68 mm to 0.92 mm. Particularly at the wavelength of 0.8 mm，it is up to 81% . Due to the short response time, the grating can be expected to have important applications in high-speed optical switches, wavelength division multiplexers or optical modulators.