The forward-backward asymmetry AFB in top quark pair production, measured at the Tevatron, is probably related to the contribution of new particles. The Tevatron result is more than a 2σ deviation from the standard model prediction and motivates the application of alternative models introducing new states. However, as the standard model predictions for the total cross section σtt and invariant mass distribution M tt for this process are in good agreement with experiments, any alternative model must reproduce these predictions. These models can be placed into two categories: One introduces the s-channel exchange of new vector bosons with chiral couplings to the light quarks and to the top quark, and another relies on the t-channel exchange of particles with large flavor-violating couplings in the quark sector. In this work, we employ a model which introduces both s- and t-channel nonstandard contributions for the top quark pair production in proton-antiproton collisions. We use the minimal version of the SU(3)C-SU(3)L-U(1)X model (3-3-1 model) that predicts the existence of a new neutral gauge boson, called Z′. This gauge boson has both flavor-changing couplings to up and top quarks and chiral coupling to the light quarks and to the top quark. This very peculiar model coupling can correct the AFB for top quark pair production for two ranges of Z′ mass while leading to a cross section and invariant mass distribution quite similar to the standard model ones. This result reinforces the role of the 3-3-1 model for any new physics effect. © 2011 American Physical Society.