A search is performed for heavy neutrinos in the decay of a W boson into two muons and a jet. The data set corresponds to an integrated luminosity of approximately 3.0fb-1 of proton–proton collision data at centre-of-mass energies of 7 and 8TeV collected with the LHCb experiment. Both same-sign and opposite-sign muons in the final state are considered. Data are found to be consistent with the expected background. Upper limits on the coupling of a heavy neutrino with the Standard Model neutrino are set at 95 % confidence level in the heavy-neutrino mass range from 5 to 50GeV/c2. These are of the order of 10 - 3 for lepton-number-conserving decays and of the order of 10 - 4 for lepton-number-violating heavy-neutrino decays.