  One of the most straightforward extensions of the standard model (SM) is
having an additional Higgs doublet to the SM, namely the two Higgs doublet
models(THDM). In the type-I model, an additional Higgs doublet is introduced
that does not couple to any fermion via the Yukawa interaction. Considering
various theoretical and phenomenological constraints, we have found the
best-fitted parameter set in the type-I model using the minimum $\chi^2$ method
by scanning the model's parameter space. We show that this optimal parameter
set can be probed by precisely analyzing the decay processes $D^+ \rightarrow
\mu^+ \nu_\mu$, $B^0 \rightarrow K^* \mu^+ \mu^-$. Moreover, the decay channels
$h \rightarrow s\bar{s}$, $W^+W^-$ and $gg$ can be used to distinguish the
model from the SM. For a direct search of the model at future colliders, we
have proposed an investigation of the $e^+e^- \rightarrow t\bar{t} b\bar{b}$
process at the ILC to detect the new physics of the model. Considering the
initial state radiation correction and applying appropriate background cuts,
the calculation result of the scattering cross section shows that it is
feasible to observe a clear and unique signal in the $t\bar{b}$ invariant mass
distribution corresponding to the charged Higgs pair creations.
