We propose a model based on the gauge group $SU(3{)}_{C}\ensuremath{\bigotimes}SU(3{)}_{L}\ensuremath{\bigotimes}U(1{)}_{X}$ with an extra ${S}_{3}$ flavor symmetry, which accounts for the lepton masses and mixing. The small active neutrino masses are generated via a double seesaw mechanism. In this scenario, the spectrum of neutrinos presents very light, light and very heavy masses. The model predicts a quasidegenerate normal hierarchy active neutrino mass spectrum and the relation $\mathrm{\ensuremath{\Delta}}{m}_{21}^{2}\ensuremath{\ll}\mathrm{\ensuremath{\Delta}}{m}_{31}^{2}$ arises from effective six-dimensional operators. The obtained neutrino mixing parameters are in agreement with the neutrino oscillation experimental data. We find $CP$ violation in neutrino oscillations with a Jarlskog invariant of about $1{0}^{\ensuremath{-}2}$.