ABSTRACT Under a coronal magnetic field, we estimate the maximal jet power of the Blandford–Znajek (BZ) mechanism, Blandford–Payne (BP) mechanism, and hybrid model. The jet power of the BZ and hybrid model mechanisms depends on the spin of the black hole, while the jet power of the BP mechanism does not depend on the spin of the black hole. At high black hole spin, the jet power of the hybrid model is greater than that of the BZ and BP mechanisms. We find that the jet power of almost all gamma-ray narrow-line Seyfert 1 galaxies (γNLS1s) can be explained by the hybrid model. However, one source with jet power ∼0.1–1 Eddington luminosity cannot be explained by the hybrid model. We suggest that a magnetic field dragged inward by the accretion disc with magnetization-driven outflows may accelerate the jets in this γNLS1.