The lifetime of the B+ c meson is measured using semileptonic decays having a J/ψ meson and a muon in the final state. The data, corresponding to an integrated luminosity of 2 fb-1, are collected by the LHCb detector in pp collisions at a centre-of-mass energy of 8 TeV. The measured lifetime is τ = 509 ± 8 ± 12 fs, where the first uncertainty is statistical and the second is systematic. © 2014 The Author(s)