  We propose a supersymmetric extra U(1) model, which can generate small
neutrino masses and necessary $\mu$ terms, simultaneously. Fields including
quarks and leptons are embedded in three ${\bf 27}$s of $E_6$ in a different
way among generations. The model has an extra U(1) gauge symmetry at TeV
regions, which has discriminating features from other models studied
previously. Since a neutrino mass matrix induced in the model has a constrained
texture with limited parameters, it can give a prediction. If we impose
neutrino oscillation data to fix those parameters, a value of $\sin\theta_{13}$
can be determined. We also discuss several phenomenological features which are
discriminated from the ones of the MSSM.
