We report, for the first time to our knowledge, the demonstration of a graphene supercapacitor as a voltage-controlled saturable absorber for femtosecond pulse generation from a solid-state laser. By applying only a few volts of bias, the Fermi level of the device could be shifted to vary the insertion loss, while maintaining a sufficient level of saturable absorption to initiate mode-locked operation. The graphene supercapacitor was operated at bias voltages of 0.5-1V to generate sub-100 fs pulses at a pulse repetition rate of 4.51 MHz from a multipass-cavity Cr(4+):forsterite laser operating at 1255 nm. The nonlinear optical response of the graphene supercapacitor was further investigated by using pump-probe spectroscopy.