  We compute the energy loss of heavy quarkonia in high temperature QCD plasmas
and investigate the energy loss effects on quarkonium suppression. Based on the
effective vertex derived from the Bethe-Salpeter amplitude for quarkonium, the
collisional and radiative energy loss are determined by quarkonium-gluon
elastic scattering and the associated gluon-bremsstrahlung, respectively. In
the energy regime $E<m_{\Upsilon}^2/T$ the collisional energy loss is dominant
over the radiative one, and the total energy loss increases with the plasma
temperature and the initial energy of quarkonium. Our numerical analysis
indicates that the medium-induced energy loss of the $\Upsilon$(1S) results in
stronger suppression at higher momentum, although the energy loss effects are
found to be small compared with the previous estimates of quarkonium
dissociation in heavy-ion collisions.
