  A major contribution to the uncertainty of finite-order perturbative QCD
predictions is the perceived ambiguity in setting the renormalization scale
$\mu_r$. For example, by using the conventional way of setting $\mu_r \in
[m_t/2,2m_t]$, one obtains the total $t \bar{t}$ production cross-section
$\sigma_{t \bar{t}}$ with the uncertainty $\Delta \sigma_{t \bar{t}}/\sigma_{t
\bar{t}}\sim ({}^{+3%}_{-4%})$ at the Tevatron and LHC even for the present
NNLO level. The Principle of Maximum Conformality (PMC) eliminates the
renormalization scale ambiguity in precision tests of Abelian QED and
non-Abelian QCD theories. In this paper we apply PMC scale-setting to predict
the $t \bar t$ cross-section $\sigma_{t\bar{t}}$ at the Tevatron and LHC
colliders. It is found that $\sigma_{t\bar{t}}$ remains almost unchanged by
varying $\mu^{\rm init}_r$ within the region of $[m_t/4,4m_t]$. The convergence
of the expansion series is greatly improved. For the $(q\bar{q})$-channel,
which is dominant at the Tevatron, its 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 two. 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
$\sqrt{s}\lesssim 1$ TeV, and the resulting NLO cross-section is increased by
$\sim 20%$. As a result, a larger $\sigma_{t\bar{t}}$ is obtained in comparison
to the conventional scale-setting method, which agrees well with the present
Tevatron and LHC data. More explicitly, by setting $m_t=172.9\pm 1.1$ GeV, we
predict $\sigma_{\rm Tevatron,\;1.96\,TeV} = 7.626^{+0.265}_{-0.257}$ pb,
$\sigma_{\rm LHC,\;7\,TeV} = 171.8^{+5.8}_{-5.6}$ pb and $\sigma_{\rm
LHC,\;14\,TeV} = 941.3^{+28.4}_{-26.5}$ pb. [full abstract can be found in the
paper.]
