Measurements of normalized differential cross sections for top-quark pair production are presented as a function of the top-quark transverse momentum, and of the mass, transverse momentum, and rapidity of the t¯t system, in proton-proton collisions at a center-of-mass energy of √s = 7 TeV. The data set corresponds to an integrated luminosity of 4.6 fb-1, recorded in 2011 with the ATLAS detector at the CERN Large Hadron Collider. Events are selected in the lepton + jets channel, requiring exactly one lepton and at least four jets with at least one of the jets tagged as originating from a b-quark. The measured spectra are corrected for detector efficiency and resolution effects and are compared to several Monte Carlo simulations and theory calculations. The results are in fair agreement with the predictions in a wide kinematic range. Nevertheless, data distributions are softer than predicted for higher values of the mass of the t¯t system and of the top-quark transverse momentum. The measurements can also discriminate among different sets of parton distribution functions.