  We study that a minimal supersymmetric standard model with an extra $U(1)'$
gauge symmetry may accommodate the explicit CP violation at the one-loop level
through radiative corrections. This model is CP conserving at the tree level
and cannot realize the spontaneous CP violation for a wide parameter space at
the one-loop level. In explicit CP violation scenario, we calculate the Higgs
boson masses and the magnitude of the scalar-pseudoscalar mixings in this model
at the one-loop level by taking into account the contributions of top quarks,
bottom quarks, exotic quarks, and their superpartners. In particular, we
investigate how the exotic quarks and squarks would affect the
scalar-pseudoscalar mixings. It is observed that the size of the mixing between
the heaviest scalar and pseudoscalar Higgs bosons is changed up to 20 % by a
complex phase originated from the exotic quark sector of this model.
