We analyze dynamic properties of vertical graphene-base hot-electron transistors (GB-HETs) and consider their operation as detectors of terahertz (THz) radiation using the developed device model. The GB-HET model accounts for the tunneling electron injection from the emitter, electron propagation across the barrier layers with the partial capture into the GB, and the self-consistent oscillations of the electric potential and the hole density in the GB (plasma oscillations), as well as the quantum capacitance and the electron transit-time effects. Using the proposed device model, we calculate the responsivity of GB-HETs operating as THz detectors as a function of the signal frequency, applied bias voltages, and the structural parameters. The inclusion of the plasmonic effect leads to the possibility of the HET-GBT operation at the frequencies significantly exceeding those limited by the characteristic RC-time. It is found that the responsivity of GB-HETs with a sufficiently perfect GB 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 GB-HETs can compete with and even surpass other plasmonic THz detectors.