  In the model based on SUSY SU(5) combined with the T' family symmetry, it is
shown in Phys. Lett. B 652, 34 (2007) and Phys. Lett. B 681, 444 (2009) that
fermion mass hierarchy and mixing angles can be naturally generated in both
lepton and quark sectors compatible with various experimental measurements. But
the predicted value for the non-zero lepton mixing angle of \theta_13 \simeq
\theta_c/3\sqrt{2} contradicts the recent experimental results from Daya Bay
and RENO. We propose to introduce one more singlet flavon field in the neutrino
sector, and with its additional contribution, we are able to generate the large
mixing angle \theta_13 ~ 8^{\circ}-10^{\circ}. The analytical expressions of
the mixing angles and neutrino masses with the additional flavon field are
derived. Our numerical results show that a large region in the model parameter
space is allowed for the normal hierarchy case, while a much smaller region is
allowed for the inverted hierarchy case. In addition, the predicted value of
the solar mixing angle is not affected by the additional singlet contribution.
On the other hand, there exists a correlation between \theta_13 value and
\theta_23 - \pi/4, as a result of the additional singlet contribution. We also
make predictions for various other variables that can be potentially tested in
the future neutrino experiments such as the Dirac CP phase, which is predicted
to be in the range of \delta ~ (195^{\circ}-200^{\circ}), and the neutrinoless
double beta decay matrix element, <m_\beta\beta>. One numerical example with
the minimal \chi^2 fit is presented, and the model predictions are consistent
with all experimental results.
