The paper introduces the fabrication, characterization and analysis of a novel graphene capacitor, which can be used as an effective saturable absorber modulator in a passive Q-switched system. The photoelectric interaction mechanism of the device is studied based on its electrical transmission and spectral absorption properties. Due to the change of Fermi level and carrier density, the absorption properties of graphene in the device can be adjusted by gate voltage without changing the properties of SA material. The output characteristics of all-solid-state pulse laser can be adjusted flexibly under ultra-low electric modulation power (~13 pA current and 1 nW power). It is applied to the Nd∶ YVO₄ all solid state laser system, and the stable pulse output at 532.04 nm wavelength is achieved. The laser absorption pump power is kept constant, and the gate voltage is changed. The pulse duration of the Q-switched output can be compressed from 1.1 μs to 345 ns. This structure is expected to further promote the development of tunable pulse lasers from visible light to mid-infrared band. In particular, passive Q-switching/mode-locking devices based on graphene devices will be used in future applications such as infrared measurement, projection display, and optical modulation.