This paper proposes a theoretical model of photo-controlled quantum capacitors in double-gated graphene-insulator-graphene (DGGIG) structure for terahertz (THz) frequency and phase modulations. In the model, the current-voltage characteristics of each segment of the DGGIG structure are controlled by different gate voltages. Using the different voltages, the DGGIG structure can be used to either generate plasma oscillation waves or shift phase in the terahertz band. Not only has the DGGIG structure various electrical properties, but also the optical properties are also excellent. Photoexcitation alters carrier concentration in DGGIG channel, and thus causes the change of the quantum capacitors. We propose a photo-controlled quantum capacitor model to quantify this phenomenon. The model shows that the quantum capacitors and photoexcitation have a sublinear dependence. An example of a device based on the model is given to describe the application of photo-controlled quantum capacitors in terahertz frequency and phase modulations. The modelled device shows that photoexcitation can change the frequency and phase of the plasma oscillation waves. INDEX TERMS Graphene-insulator-graphene, phase modulation, frequency modulation, plasma oscillation waves, photo-controlled quantum capacitors, terahertz.