We studied the glow of the plasma of a pulse discharge ignited in nitrogen by high-power focused radiation of a terahertz-wave gyrotron (a radiation frequency of 0.67 GHz, a pulse duration of 20 μs, and a power of 40 kW). The pressure in the discharge chamber varied in the range 0.1–350 Torr. It was found that at high pressures (more than 50 Torr), long-term (about 1.0–1.5 ms), a non-monotonic afterglow exists after the end of the terahertz pulse, whose intensity can exceed the plasma glow intensity significantly (by several times) during the action of the terahertz radiation pulse on the plasma. At pressures below 50 Torr, the afterglow duration proves to be significantly shorter, specifically, about several tens of microseconds. The observed long-term afterglow is radiation in certain vibrational bands of the second positive system of N2 and is due, evidently, to the processes of associative excitation of electron levels in nitrogen molecules with the participation of long-living metastables N 2 A 3 Σ u + $$ {\mathrm{N}}_2\left({\mathrm{A}}^3{\varSigma}_{\mathrm{u}}^{+}\right) $$ .