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In this paper, we calculate the $t\bar{t}$ pQCD production cross-section at NNLO and determine the top-quark pole mass from recent measurements at the LHC at $\sqrt{S}=13$ TeV center-of-mass energy to high precision by applying the Principle of Maximum Conformality (PMC). The PMC provides a systematic method which rigorously eliminates QCD renormalization scale ambiguities by summing the nonconformal $β$ contributions into the QCD coupling constant. The PMC predictions satisfy the requirements of renormalization group invariance, including renormalization scheme independence, and the PMC scales accurately reflect the virtuality of the underlying production subprocesses. By using the PMC, an improved prediction for the $t\bar{t}$ production cross-section is obtained without scale ambiguities, which in turn provides a precise value for the top-quark pole mass. Moreover, the predictive power of PMC calculations that the magnitude of higher-order PMC predictions are well within the error bars predicted from the known lower-order has been demonstrated for the top-quark pair production. The resulting determination of the top-quark pole mass $m_t^{\rm pole}=172.5\pm1.4$ GeV from the LHC measurement at $\sqrt{S}=13$ TeV is in agreement with the current world average cited by the Particle Data Group (PDG). The PMC prediction provides an important high-precision test of the consistency of pQCD and the SM at $\sqrt{S}=13$ TeV with previous LHC measurements at lower CM energies.