We build a viable family symmetry 3-3-1 model based on the \(\Delta \left(27\right) \times Z_{3}\times Z_{16}\) discrete group consistent with the low energy fermion flavor data. In the model under consideration, the small active neutrino masses arise from an inverse seesaw mechanism mediated by three very light Majorana neutrinos and the observed pattern of the Standard Model (SM) fermion masses and mixing angles arises from the breaking of the \(\Delta \left( 27\right) \times Z_{3}\times Z_{16}\) discrete group at very high energy scale. The obtained values for the physical observables in the quark sector are consistent with the experimental data, whereas those ones for the lepton sector also do, only for the case of normal neutrino mass spectrum. Our model predicts an effective Majorana neutrino mass parameter of \(m_{ee}\simeq 3.7\) meV and a Jarlskog invariant of the order of \(10^{-2}\) for the normal neutrino mass spectrum.