  The decay of Higgs boson into two spin-1/2 particles provides an ideal system
to reveal quantum entanglement and Bell-nonlocality. Future $e^+e^-$ colliders
can improve the measurement accuracy of the spin correlation of tau lepton
pairs from Higgs boson decay. We show the testability of Bell inequality
through $h\to \tau\tau$ at Circular Electron Positron Collider (CEPC). Two
realistic methods of testing Bell inequality are investigated, i.e.,
T\"{o}rnqvist's method and Clauser-Home-Shimony-Holt (CHSH) inequality. In the
simulation, we take into account the detector effects of CEPC including
uncertainties for tracks and jets from $Z$ boson in the production of
$e^+e^-\to Zh$. Necessary reconstruction approaches are described to measure
quantum entanglement between $\tau^+$ and $\tau^-$. Finally, we show the
sensitivity of CEPC to the Bell inequality violation for the two methods.
