  We consider non-renormalizable interaction term as a perturbation of the
neutrino mass matrix. We assume that the neutrino masses and mixing arise
through physics at a scale intermediate between Planck scale and the
electroweak breaking scale. We also assume that, just above the electroweak
breaking scale, neutrino masses are nearly degenerate and their mixing is
bi-maximal. Quantum gravity (Planck scale effects) lead to an effective
SU(2)_{L}\times U(1) invariant dimension-5 Lagrangian involving neutrino and
Higgs fields. On symmetry breaking, this operator gives rise to correction to
the above masses and mixing. The gravitational interaction M_{X}=M_{pl}, we
find that for degenerate neutrino mass spectrum, the considered perturbation
term change the \Delta_{21}^{'}and \Delta_{31}^{'}mass square difference is
unchanged above GUT scale. The nature of gravitational interaction demands that
the element of this perturbation matrix should be independent of flavor
indices. In this letter, we study the quantum gravity effects on neutrino mass
square difference, namely modified dispersion relation for neutrino mass square
differences..
