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In the paper, we firstly improve the scale-setting procedures of theprinciple of maximum conformality (PMC) such that the correct magnitudes of the$\alpha_s$ and the $\overline{\rm MS}$ running mass ${\overline m}$ of theperturbative QCD series are determined simultaneously with the help of therenormalization group equation. By using the derived formulas, we determine thetop-quark on-shell mass via the four loop $\overline{\rm MS}$-on-shell quarkmass relation. Its prediction avoids the conventional renormalization scaleambiguity, and a more precise pQCD prediction can be achieved. By taking thetop-quark $\overline{\rm MS}$ mass fixed-point ${\overline m}_t({\overlinem}_t)=162.5^{+2.1}_{-1.5}$ GeV as an input, we obtain, $M_t\simeq172.41^{+2.21}_{-1.57}$ GeV, in which the error is the squared average of thosefrom $\Delta \alpha_s(M_Z)$, $\Delta {\overline m}_t({\overline m}_t)$, and theapproximate error from the uncalculated five-loop terms predicted by using thePad\'{e} approximation approach.

Determination of the top-quark on-shell mass $M_t$ via the scale-invariant perturbative relation to its $\overline{\rm MS}$ mass