  We calculate the coherent and incoherent production of $J/\psi$ in PbPb
ultraperipheral collisions. The production of $J/\psi$ in ultraperipheral
collsions is product of photon flux distributions and cross section of
photon-nucleus scatterings. The distributions of photon flux is computed in
light-cone perturbation theory and the cross section of photon-nucleus
scatterings is calculated in dipole model, we assume that the two gluons
exchange contribution is the coherent cross section and the large-$N_c$
contribution is the incoherent cross section in photon-nucleus scattering. The
numerical result of the rapidity distributions of $J/\psi$ production in PbPb
ultraperipheral collisions at $\sqrt{s_{NN}}=2.76$TeV are compared with the
experimental data measured by the ALICE collaboration.
