The ALICE Collaboration at the LHC has measured the J/ψ and ψ′ photoproduction at mid-rapidity in ultra-peripheral Pb–Pb collisions at √sNN = 2.76 TeV. The charmonium is identified via its leptonic decay for events where the hadronic activity is required to be mini- mal. The analysis is based on an event sample correspond- ing to an integrated luminosity of about 23 μb−1. The cross section for coherent and incoherent J/ψ production in the rapidity interval −0.9 < y < 0.9, are dσcoh/dy = J/ψ 2.38+0.34(sta+sys) mb and dσinc /dy = 0.98+0.19(sta + −0.24 J/ψ −0.17 sys) mb, respectively. The results are compared to theoretical models for J/ψ production and the coherent cross section is found to be in good agreement with those models incorporating moderate nuclear gluon shadowing at Bjorken- x around 10−3, such as EPS09 parametrization. In addition the cross section for the process γ γ → e+e− has been measured and found to be in agreement with models implementing QED at leading order.