We consider the production of charmonium by D (D) over bar annihilation dur
ing the mixed and hadronic phase of a Pb-Pb collision at LHC energy. The ca
lculations for secondary J/psi and psi' production are performed within a k
inetic model taking into account the spacetime evolution of a longitudinall
y and transversely expanding medium. It is shown that the yield of secondar
y J/psi mesons depends strongly on the J/psi dissociation cross section wit
h co-moving hadrons. Within the most likely scenario for the dissociation c
ross section it will be negligible. The secondary production of psi' mesons
, however, due to their large cross section above the threshold, can substa
ntially exceed the primary yield.