We study heavy quarkonium within the light-front Hamiltonian formalism. Our effective Hamiltonian is based on the holographic QCD confining potential and the one-gluon exchange interaction with a running coupling. The obtained spectra are compared with experimental measurements. We present a set of light-front wave functions, which exhibit rich structure and are consistent with the nonrelativistic picture. Finally, we use the wave functions to compute the charge and mass radii.