  OPERA collaboration has reported evidence of superluminal phenomenon for
neutrinos. One of the possible ways to explain the superluminality is to have
Lorentz symmetry violated. It has been shown that dispersion relations put
forwards has the problem of physics laws vary in different inertial frames
leading to conflicting results on Cherenkov-like radiation, pion decay and high
energy neutrino cosmic ray. For theories with deformed Lorentz symmetry, by
modifying conservation laws corresponding to energy and momentum in the usual
Lorentz invariant theory, it is possible to have superluminal effect and at the
same time avoid to have conflicts encountered in Lorentz violating theories. We
study dispersion relations from deformed Lorentz symmetry. We find that it is
possible to have dispersion relations which can be consistent with data on
neutrinos. We show that once the superluminality $\delta v$ as a function of
energy is known the corresponding dispersion relation in the deformed Lorentz
symmetry can be determined.
