  The spontaneous violation of the CP symmetry in the next-to-minimal
supersymmetric standard Model (NMSSM) is investigated. It is found that the
spontaneous violation of the CP symmetry can occur in the Higgs sector of the
NMSSM for a wide region of the parameter space of the model, at the 1-loop
level where the radiative corrections due to the top quark and scalar-top quark
loops are found to generate the scalar-pseudoscalar mixings between the two
Higgs doublets of the NMSSM. In our model, we assume that the masses of the
left-handed and the right-handed scalar-top quarks are not degenerate. And we
investigate our model anaytically: We derive analytical formulae of the 1-loop
mass matrix for the neutral Higgs bosons. We calculate the upper bound on the
lightest neutral Higgs boson mass under the assumption. It is found to be about
140 GeV for our choice of parameter values in the presence of the spontaneous
violation of the CP symmetry in the NMSSM. Thus, the possibility of the
spontaneous violation of the CP symmetry is not completely ruled out in the
Higgs sector of the NMSSM if the masses of the left-handed and the right-handed
scalar-top quarks are not degenerate. Further, the phenomenology of the
$K$-${\bar K}$ mixing within the context of our model is studied. The lower
bound on CP violating phase in the $K$-${\bar K}$ mixing is found to increase
if either $\tan\beta$ decreases or $A_t$ increases.
