We study the cosmological evolution of the four-dimensional universe on the
probe D3-brane in geodesic motion in the curved background of the source D
p-brane with a nonzero Neveu-Schwarz (NS) B field. The Friedman equations,
describing the expansion of the brane universe, are obtained and analyzed f
or various limits. We elaborate on corrections to the cosmological evolutio
n due to the nonzero NS B field.