  We propose a renormalizable multi-Higgs model with $A_{4}\otimes Z_{2}\otimes
Z^{\prime}_{2}$ symmetry, accounting for the experimental deviation from the
tribimaximal mixing pattern of the neutrino mixing matrix. In this framework we
study the charged lepton and neutrino masses and mixings. The light neutrino
masses are generated via a radiative seesaw mechanism, which involves a single
heavy Majorana neutrino and neutral scalars running in the loops. The obtained
neutrino mixings and mass squared splittings are in good agreement with the
neutrino oscillation experimental data for both normal and inverted hierarchy.
The model predicts an effective Majorana neutrino mass $m_{\beta\beta}=$ 4 meV
and 50 meV for the normal and the inverted neutrino spectrum, respectively. The
model also features a suppression of CP violation in neutrino oscillations, a
low scale for the heavy Majorana neutrino (few TeV) and, due to the unbroken
$Z_2$ symmetry, a natural dark matter candidate.
