  Based on the weakly-coupled two-Higgs-doublet model with spontaneous
CP-violation (named Lee model) and the mechanism to generate the correlation
between smallness of CP-violation and lightness of scalar mass, as we proposed
earlier, we predicted a light CP-mixing scalar $\eta$ in which pseudoscalar
component is dominant. It is a natural scenario in which
$m_{\eta}\sim\mathcal{O}(10\textrm{GeV})\ll v$. Masses of all other scalars
($h$, $H$, $H^\pm$) should be around the electro-weak scale $v$. Among them,
the 125 GeV Higgs ($h$) couplings are standard-model like, and the charged
Higgs ($H^\pm$) mass should be around the heaviest neutral scalar ($H$) mass.
We discussed all experimental constraints and showed that this scenario is
still allowed by data. The strictest constraints come from the experiments of
the flavor-changing processes and the EDM of lepton and neutron. We also
discussed the future tests for this scenario. It is possible to discover the
extra scalars or exclude this scenario at future colliders, especially at the
LHC and $e^+e^-$ colliders with $\mathcal{O}(\textrm{ab}^{-1})$ luminosity. We
also pointed out that the $Z$-mediated Higgs pair production via
$e^+e^-\rightarrow h_ih_j$ ($h_i, h_j$ stand for two of the $\eta, h, H$) would
be the key observable to confirm or exclude CP-violation in Higgs sector. The
sensitivity to test this scenario is worth further studying in greater detail.
