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We study cold and hot nuclear matter effects on charmonium production in p+Pb collisions at sNN=5.02 TeV in a transport approach. At the forward rapidity, the cold medium effect on all the cc¯ states and the hot medium effect on the excited cc¯ states only can explain well the J/ψ and ψ′ yield and transverse momentum distribution measured by the ALICE collaboration, and we predict a significantly larger ψ′ pT broadening in comparison with J/ψ. However, we can not reproduce the J/ψ and ψ′ data at the backward rapidity with reasonable cold and hot medium effects.