A measurement of the b-hadron production cross section in proton-proton collisions at root s = 7 TeV 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(T)(mu) > 6 GeV with respect to the beam direction and pseudorapidity vertical bar eta(mu)vertical bar < 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 sigma(pp -> b + X -> mu + X') = 1.32 +/- 0.01(stat) +/- 0: 30(syst) +/- 0.15(lumi)mu b.