Extending a method developed by Sasaki in the Schwarzschild case and by Shibata, Sasaki, Tagoshi, and Tanaka in the Kerr case, we calculate the post-Newtonian expansion of the gravitational wave luminosities from a test particle in circular orbit around a rotating black hole up to [Formula presented] beyond the quadrupole formula. The orbit of a test particle is restricted on the equatorial plane. We find that spin-dependent terms appear in each post-Newtonian order, and that at [Formula presented] they have a significant effect on the orbital phase evolution of coalescing compact binaries. By comparing the post-Newtonian formula of the luminosity with numerical results we find that, for [Formula presented], the spin-dependent terms at [Formula presented] and [Formula presented] improve the accuracy of the post-Newtonian formula significantly, but those at [Formula presented] do not improve. © 1996 The American Physical Society.