Based on a kinetic description of J/psi dissociation and production in an expanding quark-gluon plasma that is described by a 2+1 dimensional ideal hydrodynamics, we have studied the hot medium effects on J/psi production in p+Pb collisions at sqrt{s_{NN}}=5.02 TeV. Including also the cold nuclear matter effects, we are able to reproduce recent experimental results on the nuclear modification factor R_{pPb}(J/psi) measured by the ALICE Collaboration. We have also made predictions for the R_{pPb} of J/psi and the double ratio R_{pPb}^{pro}(psi)/R_{pPb}^{pro}(J/psi) of prompt quarkonia produced in the most central 10% p+Pb collisions. We find that different from the cold nuclear matter effects, the R_{pPb}(J/psi) is slightly smaller than that in the minimum bias collisions, and the double ratio is significantly less than one at backward rapidity.
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