  The Higgs-top coupling plays a central role in the hierarchy problem and the
vacuum stability of the Standard Model (SM). We propose a central-edge
asymmetry ($A_{CE}$) to probe the CP violating Higgs-top coupling in dileptonic
channel of $t\bar{t}h(\to b\bar{b})$ production at the LHC. We demonstrate that
the CP-violating Higgs-top coupling can affect the central-edge asymmetry
through distorting $\Delta y_{\ell^+\ell^-}$ distribution because of the
contribution of new top charge asymmetric term. Since $\Delta y_{\ell^+\ell^-}$
distribution is frame-independent and has a good discrimination even in boosted
regime, we use the jet substructure technique to enhance the observability of
the dileptonic channel of $t\bar{t}h$ production. We find that (1) the
significance of dileptonic channel of $t\bar{t}h$ production can reach
$5\sigma$ for CP phase $\xi=0,\pi/4,\pi/2$ when the luminosity ${\cal
L}=795,993,1276$ fb$^{-1}$ at 14 TeV LHC. (2) the central-edge asymmetry
$A_{CE}$ show a good discrimination power of CP phase of $t\bar{t}h$
interaction, which are -40.26\%, -26.60\%, -9.47\% for $\xi=0$, $\pi/4$, $
\pi/2$ respectively and are hardly affected by the event selections. Besides,
by performing the binned-$\chi^2$ analysis of $\Delta y_{\ell^+\ell^-}$
distribution, we find that the scalar and pseudo-scalar interactions can be
distinguished at 95\% C.L. level at 14 TeV HL-LHC.
