  We show a new and simple model which induces large Majorana masses of
right-handed neutrinos. It is based on U(1)_X anomalous gauge symmetry, which
is cancelled by the Green-Schwarz mechanism. These Majorana masses can solve
the solar neutrino problem by the vacuum oscillation mechanism. The
superpotential of this model is scale invariant. The field contents are simple
extensions of the MSSM, which have four standard gauge singlet fields, two
extra vector-like fields, and right-handed neutrinos in addition to the MSSM.
