The production cross-sections of B mesons are measured in p p collisions at a centre-of-mass energy of 7 TeV, using data collected with the LHCb detector corresponding to a integrated luminosity of 0.36 fb(-1). The B+, B-0 and B-s(0) mesons are reconstructed in the exclusive decays B+ -> J/psi K+, B-0 -> J/psi K*(0) and B-s(0) -> J/psi phi, with J/psi -> mu(+)mu(-), K*(0) -> K+pi(-) and phi -> K+K-. The differential cross-sections are measured as functions of B meson transverse momentum p(T) and rapidity y, in the range 0 < p(T) < 40 GeV/c and 2.0 < y < 4.5. The integrated cross-sections in the same p(T) and y ranges, including charge-conjugate states, are measured to be sigma(pp -> B+ + X) = 38.9 +/- 0.3 (stat.) +/- 2.5 (syst.) +/- 1.3 (norm.) mu b, sigma(pp -> B-0 + X) = 38.1 +/- 0.6 (stat.) +/- 3.7 (syst.) +/- 4.7 (norm.) mu b, sigma(pp -> B-s(0) + X) = 10.5 +/- 0.2 (stat.) +/- 0.8 (syst.) +/- 1.0 (norm.) mu b, where the third uncertainty arises from the pre- existing branching fraction measurements.