Giant second-harmonic generation in the terahertz (THz) frequency range is observed in a thin film of an s-wave superconductor NbN, where the time-reversal (T) and space-inversion (P) symmetries are simultaneously broken by supercurrent injection. We demonstrate that the phase of the second-harmonic signal flips when the direction of supercurrent is inverted; ie, the signal is ascribed to the nonreciprocal response that occurs under broken P and T symmetries. The temperature dependence of the SH signal exhibits a sharp resonance, which is accounted for by the vortex motion driven by the THz electric field in an anharmonic pinning potential. The maximum conversion ratio η SHG reaches≈ 10− 2 in a thin film NbN with the thickness of 25 nm after the field cooling with a very small magnetic field of≈ 1 Oe, for a relatively weak incident THz electric field of 2.8 kV/cm at 0.48 THz.