  We find that, at the one-loop level, the spontaneous CP violation is possible
in a supersymmetric standard model that has an extra chiral Higgs triplet with
hypercharge Y=0. At the tree level, this triplet-extended supersymmetric
standard model (TESSM) cannot have any reasonable parameter spaces for the
spontaneous CP violation, because the experimental constraints on the coupling
coefficient of the neutral Higgs boson to a pair of $Z$ bosons exclude them. By
contrast, at the one-loop level, we find that there are experimentally allowed
parameter regions, where the spontaneous CP violation may take place. The mass
of the lightest neutral Higgs boson in the TESSM in this case may be as large
as about 100 GeV, by considering the one-loop contribution due to the top quark
and squark loops.
