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.
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