Measurements of b-hadron masses are performed with the exclusive decay modes B+ -> J/psi K+, B0 -> J/psi K*0, B0 -> J/psi K0S, B0_s -> J/psi phi and Lambda_b -> J/psi Lambda using an integrated luminosity of 35 pb-1 collected in pp collisions at a centre-of-mass energy of 7 TeV by the LHCb experiment. The momentum scale is calibrated with J/psi -> mu+mu- decays and verified to be known to a relative precision of 2 x 10^-4 using other two-body decays. The results are more precise than previous measurements, particularly in the case of the B0_s and Lambda_b masses.