© 2012, CERN for the benefit of the LHCb collaboration. The differential cross-section for the inclusive production of ψ(2S) mesons in pp collisions at √s = 7 TeV has been measured with the LHCb detector. The data sample corresponds to an integrated luminosity of 36 pb−1. The ψ(2S) mesons are reconstructed in the decay channels ψ(2S)→μ + μ − and ψ(2S)→J/ψπ + π −, with the J/ψ meson decaying into two muons. Results are presented both for promptly produced ψ(2S) mesons and for those originating from b-hadron decays. In the kinematic range pT(ψ(2S)) ≤ 16 GeV/c and 2 < y(ψ(2S)) ≤ 4.5 we measure σprompt(ψ(2S)) = 1.44 ± 0.01 (stat) ± 0.12 (syst) +0.20−0.40 (pol) μb, σb(ψ(2S)) = 0.25 ± 0.01 (stat) ± 0.02 (syst) μb, where the last uncertainty on the prompt cross-section is due to the unknown ψ(2S) polarization. Recent QCD calculations are found to be in good agreement with our measurements. Combining the present result with the LHCb J/ψ measurements we determine the inclusive branching fraction B(b→ψ(2S)X) = (2.73 ± 0.06 (stat) ± 0.16 (syst) ± 0.24 (BF)) × 10−3, where the last uncertainty is due to the B(b → J/ψX), B(J/ψ →μ + μ −) and B(ψ(2S)→e + e −) branching fraction uncertainties.