  The possibility of a strongly first-order electroweak phase transition is
established in the minimal supersymmetric standard model with an extra $U(1)'$,
where a nontrivial CP violating phase is introduced in its Higgs sector. We
find that there is a wide region in the parameter space of the model that
allows the strongly first-order electroweak phase transition. The mass of stop
quark need not be smaller than the top quark mass to ensure the first-order
electroweak phase transition be strong. The effect of the CP violating phase
upon the strength of the phase transition is discovered. The strength of the
phase transition is reduced when the size of the CP violation is increased. For
a given CP violating phase, we find that the model has a larger mass for the
lightest Higgs boson when it has a stronger phase transition.
