  In the framework of type-II two-Higgs-doublet model with a scalar dark matter
($S$), we examine the wrong sign Yukawa coupling of the 125 GeV Higgs which is
the only portal between the dark matter and SM sectors. After imposing the
constraints from the Higgs searches at the LHC and dark matter experiments, we
obtain some interesting observables: (i) The theory, oblique parameters, and
the Higgs searches at the LHC can impose stringent constraints on $\tan\beta$
in the case of the wrong sign Yukawa coupling of the 125 GeV Higgs. For
example, for $m_H=600$ GeV and 140 GeV $<m_A<200$ GeV, $\tan\beta$ is required
to be in the range of 4.2 and 5.7. (ii) Due to the contribution of $SS\to AA$
annihilation channel to the relic density, the dark matter coupling with the
125 GeV Higgs can be sizably suppressed. However, the $SS\to AA$ channel can
not solve the tension between the relic density and the signal data of 125 GeV
Higgs for $m_S < 50$ GeV. (iii) The limits of XENON1T (2017) and PandaX-II
(2017) exclude most of samples in the ranges of 65 GeV $<m_S<$ 78 GeV,
$0.8<f^n/f^p<1$, and $y_d/y_u>-0.82$. (iv) The Fermi-LAT limits exclude most of
samples in the range of 62.5 GeV $<m_S <65$ GeV, including the samples with
$f^n/f^p\sim -0.7$.
