In the quantum theory of gravity, for photons we expect the Lorentz Invariance Violation (LIV) and the modification of the dispersion relation between energy and momentum. 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 of 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, and Union2 Type Ia supernovae data to constrain both the model parameters and the LIV effect. We find no evidence of the LIV.
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