  We build the first 3-3-1 model based on the $\Delta (27)$ discrete group
symmetry, consistent with fermion masses and mixings. In the model under
consideration, the neutrino masses are generated from a combination of type-I
and type-II seesaw mechanisms mediated by three heavy right-handed Majorana
neutrinos and three $SU(3)_{L}$ scalar antisextets, respectively. Furthermore,
from the consistency of the leptonic mixing angles with their experimental
values, we obtain a non-vanishing leptonic Dirac CP violating phase of
$-\frac{\pi }{2}$. Our model features an effective Majorana neutrino mass
parameter of neutrinoless double beta decay, with values $m_{\beta \beta }=$ 10
and 18 meV for the normal and the inverted neutrino mass hierarchies,
respectively.
