In my previous work [Phys. Rev. D 63, 085010 (2001)], I showed that the bra
ne universe on the giant graviton moving in the near-horizon background of
the dilatonic D(6-p)-brane is described by mirage cosmology. We study the t
hermodynamic properties of the moving giant graviton by applying the thermo
dynamics of cosmology and the recently proposed holographic principles of c
osmology. We find that the Fischler-Susskind holographic bound is satisfied
by the closed brane universe on the moving giant graviton with p > 3. The
Bekenstein and the Hubble entropy bounds and the recently proposed Verlinde
holographic principle applied to the brane universe on the giant graviton
are also studied.