  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.
