  The OPERA collaboration recently reported that muon neutrinos could be
superluminal. More recently, Cohen and Glashow pointed that such superluminal
neutrinos would be suppressed since they lose their energies rapidly via
bremsstrahlung. In this Letter, we propose that Finslerian nature of spacetime
could account for the superluminal phenomena of particles. The Finsler
spacetime permits the existence of superluminal behavior of particles while the
casuality still holds. A new dispersion relation is obtained in a class of
Finsler spacetime. It is shown that the superluminal speed is linearly
dependent on the energy per unit mass of the particle. We find that such a
superluminal speed formula is consistent with data of OPERA, MINOS and
Fermilab-1979 neutrino experiments as well as observations on neutrinos from
SN1987a.
