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, B0s -> 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 B0s and {\Lambda}b masses.