We demonstrate an all-optical terahertz modulator based on single-layer graphene on germanium (GOG), which can be driven by a 1.55 μm CW laser with a low-level photodoping power. Both the static and dynamic THz transmission modulation experiments were carried out. A spectrally wide-band modulation of the THz transmission is obtained in a frequency range from 0.25 to 1 THz, and a modulation depth of 94% can be achieved if proper pump power is applied. The modulation speed of the modulator was measured to be ~ 200 KHz using a 340 GHz carrier. A theoretical model is proposed for the modulator and the calculation results indicate that the enhanced THz modulation is mainly due to the third order nonlinear effect in the optical conductivity of the graphene monolayer.