A search is presented for the lepton flavour violating decay B+ -> K+mu (-)tau (+) using a sample of proton-proton collisions at centre-of-mass energies of 7, 8, and 13 TeV, collected with the LHCb detector and corresponding to a total integrated luminosity of 9 fb(-1). The tau leptons are selected inclusively, primarily via decays with a single charged particle. The four-momentum of the tau lepton is determined by using B+ mesons from Bs20 -> B+K- decays. No significant excess is observed, and an upper limit is set on the branching fractionB(B+-> K+mu (-)tau (+))<3.9x10(-5)at90%confidence level.The obtained limit is comparable to the world-best limit.