We consider Z' and W' models recently proposed to explain the top forward-backward asymmetry at the Tevatron. We present the next-to-leading order QCD corrections to associated production of such vector bosons together with top quarks at the Large Hadron Collider, for centre-of-mass energies of 7 and 8 TeV. The corrections are significant, modifying the total production cross-section by 30-50%. We consider the effects of the corrections on the top and vector-boson kinematics. The results are directly applicable to current experimental searches, for both the ATLAS and CMS collaborations.