The production of J/psi mesons is studied with the LHCb detector using data from pp collisions at root s = 2.76 TeV corresponding to an integrated luminosity of 71 nb(-1). The differential cross-section for inclusive J/psi production is measured as a function of its transverse momentum p(T). The cross-section in the fiducial region 0 < p(T) < 12 GeV/c and rapidity 2.0 < y < 4.5 is measured to be 5.6 +/- 0.1 (stat) +/- 0.4 (syst) mu b, with the assumption of unpolarised J/psi production. The fraction of J/psi production from b-hadron decays is measured to be (7.1 +/- 0.6 (stat) +/- 0.7 (syst))%.