  Motivated by recent observations of non-zero $\theta_{13}$ from the Daya Bay
and RENO experiments, we propose a renormalizable neutrino model with $A_4$
discrete symmetry accounting for deviations from the tri-bimaximal mixing
pattern of neutrino mixing matrix indicated by neutrino oscillation data. In
the model, the light neutrino masses can be generated by radiative corrections,
and we show how the light neutrino mass matrix can be diagonalized by the
Pontecorvo-Maki-Nakagawa-Sakata mixing matrix whose entries are determined by
the current neutrino data including the Daya Bay result. We show that the
origin of the deviations from the TBM mixing is non-degeneracy of the neutrino
Yukawa coupling constants, and unremovable CP phases in the neutrino Yukawa
matrix give rise to both low energy CP violation measurable from neutrino
oscillation and high energy CP violation.
