  The Kaon direct CP violation $Re(\epsilon'_K/\epsilon_K)$ below the
experimental data of a $2\sigma$ in the standard model, which is calculated
using the RBC-UKQCD lattice and a large $N_c$ dual QCD, indicates the necessity
of a new physics effect. In order to resolve the insufficient
$Re(\epsilon'_K/\epsilon_K)$, we study the charged-Higgs contributions in a
generic two-Higgs-doublet model. If we assume that the origin of the
CP-violation phase is uniquely from the Kobayashi-Maskawa (KM) phase when the
constraints from the $B$- and $K$-meson mixings, $B\to X_s \gamma$, and Kaon
indirect CP violating parameter $\epsilon_K$ are simultaneously taken into
account, it is found that the Kaon direct CP violation through the
charged-Higgs effects can reach $Re(\epsilon'_K/\epsilon_K)_{H^\pm}\sim 8
\times 10^{-4}$. Moreover, with the constrained values of the parameters, the
branching ratios of the rare $K\to \pi \nu \bar\nu$ decays can be $BR(K^+\to
\pi^+ \nu \bar\nu)\sim 14 \times 10^{-11}$ and $BR(K_L\to \pi^0 \nu
\bar\nu)\sim 3.6 \times 10^{-11}$, where the results can be tested through the
NA62 experiment at CERN and the KOTO experiment at J-PARC, respectively.
