We construct a low-scale seesaw model to generate the masses of active neutrinos based on $S_4$ flavor symmetry supplemented by the $Z_2 times Z_3 times Z_4 times Z_{14}times U(1)_L$ group, capable of reproducing the low energy Standard model (SM) fermion flavor data. The masses of the SM fermions and the fermionic mixings parameters are generated from a Froggatt-Nielsen mechanism after the spontaneous breaking of the $S_4times Z_2 times Z_3 times Z_4 times Z_{14}times U(1)_L$ group. The obtained values for the physical observables of the quark and lepton sectors are in good agreement with the most recent experimental data. The leptonic Dirac CP violating phase $de _{CP}$ is predicted to be $259.579^circ$ and the predictions for the absolute neutrino masses in the model can also saturate the recent constraints.