  We investigate the possibility of electroweak phase transition in the minimal
supersymmetric standard model (MSSM) with an extra $U(1)'$. This model has two
Higgs doublets and a singlet, in addition to a singlet exotic quark superfield.
We find that at the one-loop level this model may accommodate the electroweak
phase transitions that are strongly first-order in a reasonably large region of
the parameter space. In the parameter region where the phase transitions take
place, we observe that the lightest scalar Higgs boson has a smaller mass when
the strength of the phase transition becomes weaker. Also, the other three
heavier neutral Higgs bosons get more large masses when the strength of the
phase transition becomes weaker.
