  We construct a Minimum Supersymmetry Standard Model expanded by a
non-anomalous family (NAF) U(1)'_{NAF} gauge symmetry. All gauge anomalies are
cancelled with no additional exotics other than the three right-handed
neutrinos. The FI D-terms associated with the U(1)'_{NAF} symmetry lead to
additional positive contributions to slepton squared masses. In a RG invariant
way, this thus solves the tachyonic slepton mass problem in Anomaly Mediated
Supersymmetry Breaking. In addition, the U(1)'_{NAF} symmetry naturally gives
rise to the fermion mass hierarchy and mixing angles, and determines the mass
spectrum of the sparticles. Our model also provides a counter example to the
previous claim that the only U(1)' that can give rise to realistic fermion mass
hierarchy and mixing pattern must be anomalous.
