The production of B-+/- mesons in proton-proton collisions at root 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/(sic)K-+/- mode, with J/(sic) -> mu(+)mu(-). 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 sigma(pp -> B-+/- X, 0 < p(T) < 40 GeV/c, 2.0 < y < 4.5) = 41.4 +/- 1.5 (stat.) +/- 3.1 (syst.) mu b.