We study the cosmological evolution of the closed universe on a spherical p
robe brane moving in the AdS(m)xS(n) background and the near-horizon backgr
ound of the dilatonic D-branes. The Friedmann equations describing the evol
ution of the brane universe and the effective energy density and pressure s
imulated on the probe brane due to its motion in the curved background spac
etime are obtained and analyzed. We also comment on the relevance of the sp
herical probe brane to the giant graviton for the special value of the prob
e energy.