  We propose a simple model of the neutrino mass matrix which can explain the
solar and atmospheric neutrino problems in a 3($\nu_L + \nu_R$) framework.
Assuming that only two right-handed neutrinos are heavy and a Dirac mass matrix
has a special texture, we construct a model with four light neutrinos. The
favorable structure of flavor mixings and mass eigenvalues required by those
neutrino deficits is realized as a result of the seesaw mechanism. Bi-maximal
mixing structure might be obtainable in this scheme. Since it contains a light
sterile neutrino, it has a chance to explain the LSND result successfully. We
consider an embedding of this scenario for the neutrino mass matrix into the
SU(5) grand unification scheme using the Froggatt-Nielsen mechanism based on
$U(1)_{F_1} \times U(1)_{F_2}$. Both a small mixing angle MSW solution and a
large mixing angle MSW solution are obtained for the solar neutrino problem
depending on the charged lepton mass matrix.
