The top-quark pair production cross section is measured in final states with one electron or muon and one hadronically decaying τ lepton from the process tt¯→(ℓνℓ)(τντ)bb¯, where ℓ=e,μ. The data sample corresponds to an integrated luminosity of 19.6 fb−1 collected with the CMS detector in proton–proton collisions at s=8TeV. The measured cross section σtt¯=257±3(stat)±24(syst)±7(lumi)pb, assuming a top-quark mass of 172.5 GeV, is consistent with the standard model prediction.