The correlation between the kinetic jet power P-jet, intrinsic gamma-ray luminosity (L-int), and accretion (L-disc) may reveal the underlying jet physics in various black hole systems. We study the relation between kinetic jet power, intrinsic gamma-ray luminosity, and accretion by using a large sample of jetted active galactic nuclei (AGNs), including flat-spectrum radio quasars (FSRQs), BL Lacertae objects (BL Lacs), gamma-ray narrow-line Seyfert 1 galaxies (gamma NLS1s), and radio galaxies. Our main results are as follows: (1) The slope indices of the relation between P-jet and L-int are 0.85 +/- 0.01 for the whole sample, 0.70 +/- 0.02 for the FSRQs, 0.83 +/- 0.03 for the BL Lacs, 0.68 +/- 0.11 for the gamma NLS1s, and 0.93 +/- 0.09 for the radio galaxies, respectively. The jets in gamma NLS1s and radio galaxies almost follow the same P-jet-L-int correlation that was obtained for Fermi blazars. (2) The slope indices of the relation between L-int and L-disc are 1.05 +/- 0.02 for the whole sample, 0.94 +/- 0.05 for the FSRQs, 1.14 +/- 0.05 for the BL Lacs, and 0.92 +/- 0.18 for the gamma NLS1s, respectively. The gamma NLS1s and radio galaxies almost also follow the L-int-L-disc correlation derived for Fermi blazars. (3) The jet power is larger than the luminosity of accretion discs for almost all jetted AGNs. Jet power depends on both the Eddington ratio and black hole mass. We obtain log P-jet similar to (1.00 +/- 0.02)log L-disc for the whole sample, which is consistent with the theoretically predicted coefficient. These results may imply that the jets of jetted AGNs are powered by the Blandford-Znajek mechanism.