  Based on current data of the Higgs boson search at the Large Hadron Collider,
we constrain the parameter space of the two-Higgs doublet models where a softly
broken $Z_2$ symmetry is employed to avoid flavor-changing neutral currents at
tree level. There are four types of Yukawa interactions under the $Z_2$ charge
assignments of the standard model fermions. We find that the model with type-II
Yukawa interactions can better explain the experimental data among all. In this
scenario, the couplings of the light CP-even Higgs boson $h$ with weak gauge
bosons are almost standard model-like or only slightly different in a small
range of $\tan\beta$. In particular, we scrutinize a well-constrained region
previously ignored by other analyses and study the phenomenology of the extra
Higgs bosons at the Large Hadron Collider.
