A bstract The production of B ± mesons in proton-proton collisions at $ \sqrt {s} $ = 7 TeV is studied using 35 pb −1 of data collected by the LHCb detector. The B ± mesons are reconstructed exclusively in the B ± → J/ψK ± mode, with J/ψ → μ + μ − . The differential production cross-section is measured as a function of the B ± transverse momentum in the fiducial region 0 < p T < 40 GeV / c and with rapidity 2 . 0 < y < 4 . 5. The total cross-section, summing up B + and B − , is measured to be σ ( pp → B ± X, 0 < p T < 40 GeV / c , 2 . 0 < y < 4 . 5) = 41 . 4 ± 1 . 5 (stat . ) ± 3 . 1 (syst . ) μb .