The lifetime of the B-c(+) meson is measured using semileptonic decays having a J/psi 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 collisions at a centre-of-mass energy of 8 TeV. The measured lifetime is tau = 509 +/- 8 +/- 12 fs, where the first uncertainty is statistical and the second is systematic.