  We calculate radiative corrections to the masses of the Higgs bosons in a
minimal supersymmetric model that contains an additional non-anomalous (U(1)')
gauge symmetry. With some fine-tuning of the (U(1)') charges of the Higgs
fields, it is possible to suppress the (Z)--(Z^{\prime}) mixing. We use this
fact, along with the lower bound on the lightest Higgs mass after LEPII era, as
a criterion to restrict the set of parameters in our analysis. We calculate the
mass of the lightest Higgs and its mixing with the other Higgs bosons, in a
large region of the parameter space.
