We introduce the flavor symmetry Z(M) x Z(N) x D-4 into the SU(6) x SU(2)(R) string-inspired model. The cyclic group Z(M) and the dihedral group D-4 are R symmetries, while Z(N) is a non-R symmetry. By imposing the anomaly-free conditions on the model, we obtain a viable solution under many phenomenological constraints coming from the particle spectra. For the neutrino sector, we find a LMA-MSW solution but no SMA-MSW solution. The solution includes phenomenologically acceptable results concerning fermion masses and mixings and also concerning hierarchical energy scales including the GUT scale, the mu scale and the Majorana mass scale of R-handed neutrinos.