A major contribution to the uncertainty of finite-order perturbative QCD predictions is the perceived ambiguity in setting the renormalization scale ${\ensuremath{\mu}}_{r}$. For example, by using the conventional way of setting ${\ensuremath{\mu}}_{r}\ensuremath{\in}[{m}_{t}/2,2{m}_{t}]$, one obtains the total $t\overline{t}$ production cross section ${\ensuremath{\sigma}}_{t\overline{t}}$ with the uncertainty $\ensuremath{\Delta}{\ensuremath{\sigma}}_{t\overline{t}}/{\ensuremath{\sigma}}_{t\overline{t}}\ensuremath{\sim}(\genfrac{}{}{0}{}{+3%}{\ensuremath{-}4%})$ at the Tevatron and LHC even for the present next-to next-to-leading-order level. The principle of maximum conformality (PMC) eliminates the renormalization scale ambiguity in precision tests of Abelian QED and non-Abelian QCD theories. By using the PMC, all nonconformal ${{\ensuremath{\beta}}_{i}}$ terms in the perturbative expansion series are summed into the running coupling constant, and the resulting scale-fixed predictions are independent of the renormalization scheme. The correct scale displacement between the arguments of different renormalization schemes is automatically set, and the number of active flavors ${n}_{f}$ in the ${{\ensuremath{\beta}}_{i}}$ function is correctly determined. The PMC is consistent with the renormalization group property that a physical result is independent of the renormalization scheme and the choice of the initial renormalization scale ${\ensuremath{\mu}}_{r}^{\mathrm{init}}$. The PMC scale ${\ensuremath{\mu}}_{r}^{\mathrm{PMC}}$ is unambiguous at finite order. Any residual dependence on ${\ensuremath{\mu}}_{r}^{\mathrm{init}}$ for a finite-order calculation will be highly suppressed since the unknown higher-order ${{\ensuremath{\beta}}_{i}}$ terms will be absorbed into the PMC scales' higher-order perturbative terms. We find that such renormalization group invariance can be satisfied to high accuracy for ${\ensuremath{\sigma}}_{t\overline{t}}$ at the next-to next-to-leading-order level. In this paper we apply PMC scale setting to predict the $t\overline{t}$ cross section ${\ensuremath{\sigma}}_{t\overline{t}}$ at the Tevatron and LHC colliders. It is found that ${\ensuremath{\sigma}}_{t\overline{t}}$ remains almost unchanged by varying ${\ensuremath{\mu}}_{r}^{\mathrm{init}}$ within the region of $[{m}_{t}/4,4{m}_{t}]$. The convergence of the expansion series is greatly improved. For the ($q\overline{q}$) channel, which is dominant at the Tevatron, its next-to-leading-order (NLO) PMC scale is much smaller than the top-quark mass in the small $x$ region, and thus its NLO cross section is increased by about a factor of 2. In the case of the ($gg$) channel, which is dominant at the LHC, its NLO PMC scale slightly increases with the subprocess collision energy $\sqrt{s}$, but it is still smaller than ${m}_{t}$ for $\sqrt{s}\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{TeV}$, and the resulting NLO cross section is increased by $\ensuremath{\sim}20%$. As a result, a larger ${\ensuremath{\sigma}}_{t\overline{t}}$ is obtained in comparison to the conventional scale setting method, which agrees well with the present Tevatron and LHC data. More explicitly, by setting ${m}_{t}=172.9\ifmmode\pm\else\textpm\fi{}1.1\text{ }\text{ }\mathrm{GeV}$, we predict ${\ensuremath{\sigma}}_{\mathrm{Tevatron},1.96\text{ }\mathrm{TeV}}={7.626}_{\ensuremath{-}0.257}^{+0.265}\text{ }\text{ }\mathrm{pb}$, ${\ensuremath{\sigma}}_{\mathrm{LHC},7\text{ }\mathrm{TeV}}={171.8}_{\ensuremath{-}5.6}^{+5.8}\text{ }\text{ }\mathrm{pb}$ and ${\ensuremath{\sigma}}_{\mathrm{LHC},14\text{ }\mathrm{TeV}}={941.3}_{\ensuremath{-}26.5}^{+28.4}\text{ }\text{ }\mathrm{pb}$.