In order to explore the new materials and devices that generate terahertz signals, a graphene-based Field Effect Transistor(FET) device model with double-top-gate structure is proposed, and the terahertz characteristics of the device are studied. Using the Fermi function, it is found that the device has the possibility of negative conductivity in a certain terahertz band. The relationships among graphene integrated conductivity and bias voltage, relaxation time, gate voltage and temperature are obtained, which indicate the potential of this device as a new terahertz radiation source.