  Recent observations by the Fermi-LAT showed that there are delayed arrivals
of GeV photons relative to the onset of MeV photons in some GRBs. In order to
avoid a large optical depth, the minimal value of the Lorentz factor has been
estimated to be higher than 1000 in some brightest bursts. In this paper, we
present a detailed calculation of the time delay between the MeV and GeV
photons in the framework of the magnetic-dominated jet model. We find that the
time delay strongly depends on the saturated bulk Lorentz factor of the jet.
Inspired by this fact, we use this model to calculate the Lorentz factors of
the four brightest Fermi bursts. The results indicate that the Lorentz factors
are much smaller than that obtained from the "single-zone" scenario. The short
GRB 090510 has a minimal Lorentz factor 385, while the three long bursts GRB
080916c, GRB090902b and GRB 090926 have almost the same Lorentz factors, with
an average value near 260. Another interesting result is that, for long bursts,
GeV photons are emitted after the bulk Lorentz factor saturates. For the short
GRB, however, MeV and GeV photons are emitted at the same phase, i.e., either
at the expansion phase or at the coast phase.
