We present a new measurement of the inclusive forward-backward tt̄ production asymmetry and its rapidity and mass dependence. The measurements are performed with data corresponding to an integrated luminosity of 5.3fb -1 of pp̄ collisions at √s=1.96TeV, recorded with the CDF-II Detector at the Fermilab Tevatron. Significant inclusive asymmetries are observed in both the laboratory frame and the tt̄ rest frame, and in both cases are found to be consistent with CP conservation under interchange of t and t̄. In the tt̄ rest frame, the asymmetry is observed to increase with the tt̄ rapidity difference, Δy, and with the invariant mass M tt̄ of the tt̄ system. Fully corrected parton-level asymmetries are derived in two regions of each variable, and the asymmetry is found to be most significant at large Δy and Mtt̄. For Mtt̄?450GeV/c2, the parton-level asymmetry in the tt̄ rest frame is Att̄=0.475±0.114 compared to a next-to-leading order QCD prediction of 0.088±0.013. © 2011 American Physical Society.