We propose a model based on the gauge group SU(3)(C) circle times SU(3)(L) circle times 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 Delta m(21)(2) << 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 10(-2).