  We examine the parameter space of two-Higgs-doublet model of type-II after
imposing the relevant theoretical and experimental constraints from the
precision electroweak data, $B$-meson decays, the LHC run-I and run-II data. We
find that the searches for Higgs via the
$\tau\bar{\tau},~WW,~ZZ,\gamma\gamma,~hh,~hZ,~HZ,~AZ$ channels can give strong
constraints on the CP-odd Higgs $A$ and heavy CP-even Higgs $H$, and the
parameter space excluded by each channel is respectively carved out in detail.
The surviving samples are discussed in two different of regions: (i) In the
SM-like coupling region of the 125 GeV Higgs, $m_A$ is allowed to be as low as
350 GeV, and $\tan\beta$ is imposed a strong upper limit. $m_H$ is allowed to
be as low as 200 GeV for the proper $\tan\beta$, $\sin(\beta-\alpha)$ and
$m_A$, but is required to be larger than 300 GeV for $m_A=700$ GeV. (ii) In the
wrong sign Yukawa coupling of the 125 GeV, $\tan\beta$ and $\sin(\beta-\alpha)$
can be imposed upper limits by $b\bar{b}\to A/H\to \tau\bar{\tau}$ channel and
lower limits by the $A\to hZ$ channel. $m_A$ and $m_H$ are respectively allowed
to be as low as 60 GeV and 200 GeV, but 320 GeV $< m_A<$ 500 GeV is excluded
for $m_H=$ 700 GeV.
