We introduce the flavor symmetry ZM × ZN × D4 into the SU(6) × SU(2)R string-inspired model. The cyclic group ZM and the dihedral group D4 are R symmetries, while ZN 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 μ scale and the Majorana mass scale of R-handed neutrinos.