A spectrally wide-band terahertz modulator based on monolayer graphene on germanium (GOG) is proposed. Utilizing a homemade THz-TDS (Terahertz-time domain spectroscopy) system, we experimentally demonstrated that the THz modulator can be tuned by a 1550 nm pump beam in a frequency range from 0.2 to 1.5 THz. The average transmittance of THz decreases from 40% to 22% when the pump power is increased to 250 mW, while the absorption coefficient averaged increases from 19 cm<sup>-1</sup> to 44 cm<sup>-1</sup>. The maximum modulation depth of the GOG modulator can reach as high as 62% at 0.38 THz and in a frequency range from 0.2 to 0.7 THz, the modulation depth is over 50%. Compared with bare Ge, it was proved that the modulation performance can be moderately enhanced by introducing monolayer graphene. This novel optically controlled graphene based THz modulator provides a feasible method for terahertz applications in communication and imaging.