The low intrinsic absorption and the existence of the inherent defects hamper the monoatomic layer graphene from being a high-performance photoelectric material, which leads to the strategy to form heterostructure by combining graphene with semiconductor materials. In this work, a graphene/GaAs heterostructure based photodetector has been designed and fabricated, in which the two-dimensional electron gas are enhanced to improve the photoresponse ability at the band of sub-millimeter and Terahertz (THz) wave ranging from 20 GHz to 0.12 THz. Under 25 GHz radiation, the responsivity of photodetector at room temperature (RT) reaches 20.6 V?W^-1, with the response time of 9.8 μs and the noise equivalent power (NEP) of 3.2×10¹⁰ W?Hz^-1/2 under a bias of 400 mV. At 0.12 THz, the responsivity is determined to be 4.6 V?W^-1, with the response time of 10 μs. And a NEP of 1.4×10^-9 W?Hz^-1/2 can be achieved under the bias of 400 mV. These results exhibit great application potential for the graphene/GaAs heterostructure based THz photodetectors.