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We examine the parameter space of two-Higgs-doublet model of type-II afterimposing the relevant theoretical and experimental constraints from theprecision electroweak data, $B$-meson decays, the LHC run-I and run-II data. Wefind that the searches for Higgs via the$\tau\bar{\tau},~WW,~ZZ,\gamma\gamma,~hh,~hZ,~HZ,~AZ$ channels can give strongconstraints on the CP-odd Higgs $A$ and heavy CP-even Higgs $H$, and theparameter space excluded by each channel is respectively carved out in detail.The surviving samples are discussed in two different of regions: (i) In theSM-like coupling region of the 125 GeV Higgs, $m_A$ is allowed to be as low as350 GeV, and $\tan\beta$ is imposed a strong upper limit. $m_H$ is allowed tobe 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 thewrong 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 andlower limits by the $A\to hZ$ channel. $m_A$ and $m_H$ are respectively allowedto be as low as 60 GeV and 200 GeV, but 320 GeV $< m_A<$ 500 GeV is excludedfor $m_H=$ 700 GeV.

Two-Higgs-doublet model of type-II confronted with the LHC run-I and run-II data