Terahertz plasmon emission is the key to getting terahertz radiation, which has resulted in numerous studies on it. In this paper, we present the results of a theoretical investigation of terahertz plasmon emission by drifting electrons in a grated graphene system driven by an electric field by applying the Boltzmann's equilibrium equation method. The results show that plasmon frequencies from terahertz to infrared are generated by drifting electrons through the interaction between plasmons and electrons. Obvious increase of the plasmon emission strength with the driving electric field can be seen when the electric field is more than a certain strength (e.g. 1.0 kV/cm). The effects of electron density and the grating period on the emission strength of plasmons were also investigated. It was found that terahertz plasmons can be obtained by applying a grating with appropriate period. The plasmon frequencies can be tuned using either the driving electric field or the electron density controlled by the gate voltage or the grating parameters. This work may help to gain insight into graphene plasmonics and be pertinent to the application of graphene-based structures as electrically tunable terahertz plasmonic devices.