  We study the Higgs sector in the Next-to-Minimal Supersymmetric Standard
Model with and without explicit CP violation, focusing on the case of weak
scale expectation value of the singlet field. We scan a wide range of the
parameter space to find out allowed regions by requiring that the electroweak
vacuum be the global minimum of the effective potential and that the neutral
Higgs bosons with moderate gauge coupling be heavier than the lower bound on
the Higgs boson in the standard model. Among the allowed parameters, some sets
admit the situation in which the light Higgs bosons couple with the $Z$ boson
too weak to be found in present collider experiments. For such parameter sets,
we find an upper bound on the charged Higgs mass which is reachable in LHC.
