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Terahertz detectors based on two-dimensional Dirac materials offer a new approach for room-temperature terahertz detection with high response and low noise. However, these devices can hardly show high response over a broad frequency range, mainly due to the poor absorption caused by their ultrathin nature. Here we apply metallic gratings to enhance the excitation efficiency of graphene plasmons. When nonzero source-drain bias is applied, graphene plasmons can generate terahertz response orthogonal to the polarization of the incidence. The response is attributed to the orthogonal overdamped plasmon rectification effect, and graphene plasmons-enhanced photo-thermoelectric effect. By comparing the normalized on/off ratio, the metallic gratings are found to effectively enhance the coupling efficiency between graphene plasmons and THz incidence, and thus the absorption and responsivity. The results are beneficial for improving the response of room temperature THz detectors.