  We consider the production of charmonium by $D\bar D$ annihilation during the
mixed and hadronic phase of Pb-Pb collision at LHC energy. The calculations for
secondary $J/\psi$ and $\psi^,$ production are performed within a kinetic model
taking into account the space-time evolution of a longitudinally and
transversely expanding medium. It is shown that the yield of secondary $J/\psi$
mesons depends strongly on the $J/\psi$ dissociation cross section with
co-moving hadrons. Within the most likely scenario for the dissociation cross
section it will be negligible. The secondary production of $\psi^,$ mesons,
however, due to their large cross section above the threshold, can
substantially exceed the primary yield.
