  The seesaw mechanism is the most attractive mechanism to explain the small
neutrino masses, which predicts the neutrinoless double beta decay
($0\nu\beta\beta$) of the nucleus. Thus the discovery of $0\nu\beta\beta$ is
extremely important for future particle physics. However, the present data on
the neutrino oscillation is not sufficient to predict the value of $m_{ee}$ as
well as the neutrino mass $m_\nu^i$. In this short article, by adopting a
simple and consistent Froggatt-Nielsen model, which can well explain the
observed masses and mixing angles of quark and lepton sectors, we calculate the
distribution of $m_{ee}$ and $m_\nu^i$. Interestingly, a relatively large part
of the preferred parameter space can be detected in the near future.
