  We study the cosmological evolution of the closed universe on a spherical
probe brane moving in the AdS$_m\times S^n$ background and the near-horizon
background of the dilatonic D-branes. The Friedmann equations describing the
evolution of the brane universe, and the effective energy density and pressure
simulated on the probe brane due to its motion in the curved background
spacetime are obtained and analyzed. We also comment on the relevance of the
spherical probe brane to the giant graviton for the special value of the probe
energy.
