  By imposing validity of the perturbation and stability of vacuum up to an
energy scale $\Lambda$ ($\leq 10^{19}$ GeV), we evaluate mass bounds of the
lightest CP-even Higgs-boson mass ($m_h$) in the two-Higgs-doublet model (2HDM)
with a softly-broken discrete symmetry. The most general bounds are obtained as
a function of $\Lambda$ vering all the free parameters under the experimental
constraint from the $rho$ parameter and the b \to s \gamma$ results. We find
that, while the upper bound is almost the same as in the SM, the lower bound is
significantly reduced. In the decoupling regime where the model behaves like
the SM at low energy, the lower bound is given, for example, by about 100 GeV
for $\Lambda = 10^{19}$ GeV and $m_t = 175$ GeV, which is smaller by about 40
GeV than the corresponding lower bound in the SM. In general case, the $m_h$ is
no longer bounded from below by these conditions. If we consider the
experimental $b \to s \gamma$ constraint, small $m_h$ are excluded in Model II
of the 2HDM.
