Giant second-harmonic generation (SHG) in the terahertz (THz) frequency range is observed in a thin film of an s-wave superconductor NbN, where the time-reversal ($mathcal{T}$-) and space-inversion ($mathcal{P}$-) symmetries are simultaneously broken by supercurrent injection. We demonstrate that the phase of the second-harmonic (SH) signal flips when the direction of supercurrent is inverted, i.e., the signal is ascribed to the nonreciprocal response that occurs under broken $mathcal{P}$- and $mathcal{T}$-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 $eta_{mathrm{SHG}}$ reaches $approx10^{-2}$ in a thin film NbN with the thickness of 25 nm after the field cooling with a very small magnetic field of $approx1$ Oe, for a relatively weak incident THz electric field of 2.8 kV/cm at 0.48 THz.
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