  Stimulated by a successful quark mass matrix model based on
U(3)$\times$U(3)$'$ family symmetry, a phenomenological neutrino mass matrix
for the Majorana neutrinos $(\nu_L, \nu_R^c, N_L, N_R^c)$ is proposed. The
model has only three adjustable parameters. Nevertheless, the model gives
reasonable predictions for the neutrino masses, mixings, and CP violating
phases in the neutrino mixing matrix.
