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We propose a supersymmetric extra U(1) model, which can generate small neutrino masses and necessary μ terms, simultaneously. Fields including quarks and leptons are embedded in three 27's of E6 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 θ13 can be determined. We also discuss several phenomenological features which are discriminated from the ones of the MSSM.