A measurement of the b-hadron production cross section in proton-proton collisions at √s = 7TeV is presented. The dataset, corresponding to 85 nb^-1, was recorded with the CMS experiment at the LHC using a low-threshold single-muon trigger. Events are selected by the presence of a muon with transverse momentum p^µ_T> 6 GeV with respect to the beam direction and pseudorapidity ι h^µ ι < 2:1. The transverse momentum of the muon with respect to the closest jet discriminates events containing b hadrons from background. The inclusive b-hadron  production cross section is presented as a function of muon transverse momentum and pseudorapidity. The measured total cross section in the kinematic acceptance is σ(pp → b + X →µ + X′) = 1:32 ± 0:01(stat) ± 0:30(syst) ±0:15(lumi)µb.