Top-quark pair production cross section is measured in final states with one electron or muon and one hadronically decaying tau lepton from the process t bar t ->(lv(sup l))(tau v(sup tau))b bar b, where l-e, tau. The data sample corresponds to an integrated luminosity of 19.6 fb(sub -1) collected with the CMS detector in proton-proton collisions at square root s=8 TeV. The measured cross section sigma(sup t bar t)=257 plus or minus 3(stat)plus or minus 24(syst) plus or minus 7(lumi) pb, assuming a top-quark mass of 172.5 GeV, is consistent with the standard model prediction.