  We obtain modified dispersion relations by requiring the vanishing of
determinant of inverse of modified photon propagators in Lorentz invariance
violation (LIV) theory. Inspired by these dispersion relations, we give a more
general dispersion relation with less assumption and apply it to the recent
observed gamma-ray burst GRB090510 to extract various constraints on LIV
parameters. We find that the constraint on quantum gravity mass is slightly
larger than the Planck mass but is consistent with the other recent
observations, so the corresponding LIV coefficient $\xi_1$ has reached the
natural order ($o(1)$) as one expects. From our analysis, the linear LIV
corrections to photon group velocity might be not excluded yet.
