Same- and opposite-sign charge asymmetries are measured in lepton+jets tt¯ events in which a b-hadron decays semileptonically to a soft muon, using data corresponding to an integrated luminosity of 20.3 fb−1 from proton-proton collisions at a centre-of-mass energy of √s=8 TeV collected with the ATLAS detector at the Large Hadron Collider at CERN. The charge asymmetries are based on the charge of the lepton from the top-quark decay and the charge of the soft muon from the semileptonic decay of a b-hadron and are measured in a fiducial region corresponding to the experimental acceptance. Four CP asymmetries (one mixing and three direct) are measured and are found to be compatible with zero and consistent with the Standard Model.