  Possible Lorentz invariance violation (LIV) has been investigated for a long
time based on observations of GRBs . These arguments relied on the assumption
that photons with different energy are emitted at the same place and time. In
this work, we try to take account of the intrinsic time delay $\Delta t_{\rm
int}$ between emissions of low and high energy photons by using the magnetic
jet model. The possible LIV effects are discussed in a unified scenario both
for long and short {\it Fermi}-detected GRBs. This leads to a unique quantum
gravity energy scale $M_1c^2 \sim 1.0 \times 10^{20}$ GeV respecting the linear
dispersion relation.
