  We study the LHC searches for the heavy $CP$-odd Higgs boson $A$ and
$CP$-even Higgs boson $H$ in the context of general two-Higgs-doublet model.
Specifically, we consider the decay mode of $A/H\to t \bar t $ through the $b
\bar b$ or $t \bar t $ associated production channels. In the so-called
"alignment limit" of the two-Higgs-doublet model, this decay mode can be the
most dominant one. By employing the HEPTopTagger and the
multi-variable-analysis method, we present the search sensitivities for both
$CP$-odd Higgs boson $A$ and $CP$-even Higgs boson $H$ via these channels at
the high-luminosity LHC runs.
