The W and Z boson production was measured via the muonic decay chan- nel in proton-lead collisions at √sNN = 5.02 TeV at the Large Hadron Collider with the ALICE detector. The measurement covers backward (−4.46 < ycms < −2.96) and for- ward (2.03 < ycms < 3.53) rapidity regions, corresponding to Pb-going and p-going direc- tions, respectively. The Z-boson production cross section, with dimuon invariant mass of 60 < mμμ < 120GeV/c2 and muon transverse momentum (pμT) larger than 20GeV/c, is measured. The production cross section and charge asymmetry of muons from W-boson decays with pμT > 10 GeV/c are determined. The results are compared to theoretical calcu- lations both with and without including the nuclear modification of the parton distribution functions. The W-boson production is also studied as a function of the collision centrality: the cross section of muons from W-boson decays is found to scale with the average number of binary nucleon-nucleon collisions within uncertainties.