  We present the results of quenched charmonium spectrum for S- and P-states,
obtained by a relativistic heavy quark method on anisotropic lattices.
Simulations are carried out using the standard plaquette gauge action and a
meanfield-improved clover quark action at $a_t^{-1} = 3$--6 GeV with the
renormalized anisotropy fixed to $\xi \equiv a_s/a_t =3$. We study the scaling
of our fine and hyperfine mass splittings, and compare with previous results.
