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We propose a graphene-based terahertz (THz) photodetector with a microstructure array designed to manipulate the surface electromagnetic modes. Benefiting from the generated localized electromagnetic resonance, a nearly perfect absorption to the incident THz radiation is observed, an asymmetrical temperature distribution is realized along the graphene channel under uniform THz illumination, and thereby an obvious photothermoelectric response is achieved. Polarization and geometry dependence of the photovoltage provides evidence that the photoresponse originated from the localized electromagnetic resonance. Our method is also suitable for other two-dimensional materials and shows promising applications for THz detection.