The production of psi(2S) mesons is studied in dimuon final states using proton-lead (pPb) collision data collected by the LHCb detector. The data sample corresponds to an integrated luminosity of 1.6 nb(-1). The nucleon-nucleon centre-of-mass energy of the pPb collisions is root s(NN) = 5 TeV. The measurement is performed using psi(2S) mesons with transverse momentum less than 14 GeV/c and rapidity y in the ranges 1.5 < y < 4.0 and -5.0 < y < -2.5 in the nucleon-nucleon centre-of-mass system. The forward-backward production ratio and the nuclear modi fi cation factor are determined for psi(2S) mesons. Using the production cross-section results of psi(2S) and J/psi mesons from b-hadron decays, the b (b) over bar cross-section in pPb collisions at root s(NN) = 5 TeV is obtained.