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 model accounts for the carrier statistics, tunneling injection from the emitter, electron propagation across the barrier layer with partial capture into the graphene-layer (GL) base, and the self-consistent plasma oscillations of the electric potential and the hole density in the GL-base. The calculated responsivity of the HET-GBT THz detectors as a function of the signal frequency 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.