  Charmonia produced in initial hard parton scatterings during heavy ion
collisions move with respect to the medium rather than flow with the medium.
Lattice studies suggest that charmonium bound states at the rest are
dissociated at $T\gtrsim 1.5 T_c$. We present results on momentum dependences
of charmonium properties in a hot medium from lattice QCD Monte Carlo
simulations. The dispersion relation of the screening mass and the change of
correlation and spectral functions at various temperatures and momenta are
discussed.
