The topcolour-assisted technicolour (TC2) model is an interesting dynamical theory among the various new physics models. We calculate the total t(t) cross section and the relative correction of the TC2 model to the cross section at Tevatron Run Ⅱ and LHC. At the Tevatron Run Ⅱ, the cross section predicted by the standard model (SM) is consistent with the experimental data, and in most parameter spaces of the TC2 model, the relative correction of the TC2 model to the cross section is too small to be detectable. We find that the t(t) cross section is more sensitive to the parameters of the TC2 model at the LHC and the relative correction of the TC2 model to the cross section is over 10% in general. Such a value of the relative correction should be large enough to be detectable at the LHC. Therefore, it is promising to find the clue of the TC2 model via the t(t) production at the LHC.