  In quantum theory of gravity, we expect the Lorentz Invariance Violation
(LIV) and the modification of the dispersion relation between energy and
momentum for photons. The effect of the energy-dependent velocity due to the
modified dispersion relation for photons was studied in the standard
cosmological context by using a sample of Gamma Ray Bursts (GRBs). In this
paper we mainly discuss the possible LIV effect by using different cosmological
models for the accelerating universe. Due to the degeneracies among model
parameters, the GRBs' time delay data are combined with the cosmic microwave
background data from the Planck first year release, the baryon acoustic
oscillation data at six different redshifts, as well as Union2 type Ia
supernovae data, to constrain both the model parameters and the LIV effect. We
find no evidence of LIV.
