The production of B +/- mesons is studied in pp collisions at centre-of-mass energies of 7 and 13 TeV, using B-+/- -> J/psi K-+/- decays and data samples corresponding to 1.0 fb(-1) and 0.3 fb(-1), respectively. The production cross-sections summed over both charges and integrated over the transverse momentum range 0 < pT < 40 GeV/c and the rapidity range 2.0 < y < 4.5 are measured to be sigma-(pp -> B-+/- X, root s = 7 TeV) = 43.0 +/- 0.2 +/- 2.5 +/- 1.7 mu b, sigma(pp -> B-+/- X, root s = 13 TeV) = 86.6 +/- 0.5 +/- 5.4 +/- 3.4 mu b, where the first uncertainties are statistical, the second are systematic, and the third are due to the limited knowledge of the B-+/- -> J/psi K-+/- branching fraction. The ratio of the cross-section at 13 TeV to that at 7 TeV is determined to be 2.02 +/- 0.02 (stat) +/- 0.12 (syst). Differential cross-sections are also reported as functions of pi, and y. All results are in agreement with theoretical calculations based on the state-of-art fixed next-to-leading order quantum chromodynamics.