We study the effect of tt̄Z axial-vector coupling to the tt̄ pair production process near threshold at e+e- colliders. P-wave resonance states produced via axial-vector coupling interfere with S-wave resonance states due to the large top-quark width. This interference gives rise to the forward-backward asymmetry below threshold which grows from 0 to ∼ 7% as mt is increased from 100 to 200 GeV. Its αs dependence is magnified simultaneously. The measurement of the forward-backward asymmetry may allow an efficient determination of αs for a relatively heavy top quark.