  We show that the neutrino mass matrix of the Zee-Babu model is able to fit
the recent data on neutrino masses and mixing with non-zero $\theta_{13}$ in
the inverted neutrino mass hierarchy. The results show that the Majorana phases
are equal to zero and the Dirac phase ($\de$) is predicted to either $0$ or
$\pi$, i. e, there is no CP violation in the Zee-Babu model at the two loop
level. The effective mass governing neutrinoless double beta decay and the sum
of neutrino masses are consistent with the recent analysis.
