We evaluate the operation of vertical hot-electron graphene-base transistors (HET-GBTs) as detectors of terahertz (THz) radiation using the developed device model. The calculated responsivity of the HET-GBT THz detectors exhibits sharp resonant maxima in the THz range of frequencies associated with the excitation of plasma oscillations. The positions of these maxima are controlled by the applied bias voltages. The HET-GBTs can compete with and even surpass other plasmonic THz detectors.