A measurement is presented of the tt ¯ inclusive production cross section in pp collisions at a center-of-mass energy of s √ =8  TeV using data collected by the ATLAS detector at the CERN Large Hadron Collider. The measurement was performed in the lepton+jets final state using a data set corresponding to an integrated luminosity of 20.3  fb −1 . The cross section was obtained using a likelihood discriminant fit and b -jet identification was used to improve the signal-to-background ratio. The inclusive tt ¯ production cross section was measured to be 260±1(stat) +22 −23 (stat)±8(lumi)±4(beam)  pb assuming a top-quark mass of 172.5 GeV, in good agreement with the theoretical prediction of 253 +13 −15   pb . The tt ¯ →(e,μ)+jets production cross section in the fiducial region determined by the detector acceptance is also reported.