We present the results of quenched charmonium spectrum for S- and P-states,
obtained by a relativistic heavy quark method on anisotropic lattices. Sim
ulations are carried out using the standard plaquette gauge action and a me
anfield-improved clover quark action at a(t)(-1) = 3-6 GeV with the renorma
lized anisotropy fixed to xi drop a(s)/a(t) = 3. We study the scaling of ou
r fine and hyperfine mass splittings, and compare with previous results.