Detection of the terahertz (THz) electromagnetic spectrum(wavelengths range 0.03-3 mm) is a promising technique for a large variety of strategic applications, such as biomedical diagnostics and process, quality control, homeland security, and environmental monitoring, etc. Graphene has been recognized internationally to have dominant advantages in photodetectors operating due to its high carrier mobility, gapless spectrum, and frequency-independent absorption coefficient. Graphene photodetector operating in the THz region has been extensively studied with great interests. A graphene microcavity photodetector with THz electromagnetic spectrum is demonstrated in this paper, and its responsivity and detectivity under THz electromagnetic spectrum are evaluated. In the designed device, we adopt a distributed bragger reflection (DBR) consisting of two semiconductor materials SiO2 and TiO2 to form an alternating cavity with high-finesse planar, sandwich the absorbing graphene layer between the cavitys top and bottom layers, and design the DBRs reflectivity by the optical transmission matrix method. The monolayer graphenes optical absorption mechanism of the THz radiation spectrum is studied by the conductivity matrix and Maxwells equations with the electromagnetic boundary conditions. Graphenes transfer matrix and absorption coefficient equation are further derived. It is found that at THz region, graphenes conductivity plays an important role in its absorptionand its absorption is 9-22 times enhanced compared with that at the visible region. An optical absorption model of microcavity-enhanced graphene photodetector at THz region is established. The photodetectors absorption rate and responsitivity are analyzed specifically. Theoretical analysis shows that absorption rate is symmetrical to the microcavitys center position and changes periodically, and the shift of the microcavity length influences the period numbers. The maximum rate of the photodetectors absorption reaches 0.965 at 0.12 THz, which increases 93% compared with its maximum absorption rate 0.5 with no cavity. The optimal structure parameters for the designed photodetector are as follows, the top and bottom mirrors reflectivity are 0.928 and 0.998 respectively, the microcavity length is 2.5 mm, the graphene is 0.035 mm away from the top mirror. Under the optimal structure, the photodetectors responsivity reaches 236.7 A/W, and its full width at half maximum reaches 0.035 THz. The designed graphene microcavity photodetector can exhibit high responsivity and detectivity in THz radiation spectrum.