  The bottom quark forward-backward asymmetry ($A_{FB}^b$) data at LEP exhibits
a long-standing discrepancy with the standard model prediction. We propose a
novel method to probe the $Zb\bar{b}$ interactions through $gg\to Zh$
production at the LHC, which is sensitive to the axial-vector component of the
$Zb\bar{b}$ couplings. We demonstrate that the $Zh$ data collected at the 13
TeV LHC can already resolve the apparent degeneracy of the anomalous
$Zb\bar{b}$ couplings implied by the LEP precision electroweak measurements,
with a strong dependence on the observed distribution of the $Z$ boson
transverse momentum. We also show the potential of the HL-LHC to either verify
or exclude the anomalous $Zb\bar{b}$ couplings observed at LEP through
measuring the $Zh$ production rate at the HL-LHC, and this conclusion is not
sensitive to possible new physics contribution induced by top quark or Higgs
boson anomalous couplings in the loop.
