Effective high-capacity data management necessitates the use of ultrafast fiber lasers with mode-locking-based femtosecond pulse generation. We suggest a simple but highly efficient structure of a graphene saturable absorber in the form of a graphene/poly(methyl methacrylate) (PMMA)/graphene capacitor and demonstrate the generation of ultrashort pulses by passive mode-locking in a fiber ring laser cavity, with simultaneous electrical switching (on/off) of the mode-locking operation. The voltage applied to the capacitor shifts the Fermi level of the graphene layers, thereby controlling their nonlinear light absorption, which is directly correlated with mode-locking. The flexible PMMA layer used for graphene transfer also acts as a dielectric layer to realize a very simple but effective capacitor structure. By employing the graphene capacitor on the polished surface of a D-shaped fiber, we demonstrate the switching of the mode-locking operation reversibly from the femtosecond pulse regime to a continuous wave regime of the ring laser with an extinction ratio of 70.4 dB.