  Radiative symmetry breaking is studied in a superstring-inspired
supersymmetric model which is extended with a low energy extra $U(1)$ symmetry.
In this model the $\mu$-problem is radiatively solved in an automatic way. The
right-handed neutrino can be heavy and the seesaw mechanism will produce the
small neutrino mass which makes the MSW solution applicable to the solar
neutrino problem. We search a parameter region which has the favorable feature
for the radiative symmetry breaking at the weak scale. Rather wide parameter
region is found to be allowed. The upper bound of the extra $Z$ boson mass is
estimated as $M_{Z_2} \le 2000$~GeV for a top mass range $ 150~{\rm GeV} \le
m_t \le 190~{\rm GeV}$. Some phenomenological features of the extra $Z$ boson
are also presented.
