  The last phase transition predicted by the standard model of particle physics
took place at the QCD scale $T\sim200$ MeV when the universe was about
$t\sim10^{-5}$ seconds old and the Hubble radius was around 10 Km. In this
paper, we consider the quark--hadron phase transition in the context of
brane-world cosmology where our universe is a 3-brane embedded in a
$m$-dimensional bulk and localization of matter on the brane is achieved by
means of a confining potential. We study the behavior of the physical
quantities relevant to the description of the early universe like the energy
density, temperature and scale factor, before, during, and after the phase
transition and investigate the effects of extrinsic curvature on the
cosmological phase transition. We show that the brane-world effects reduce the
effective temperature of the quark--gluon plasma and of the hadronic fluid.
Finally, we discuss the case where the universe evolved through a mixed phase
with a small initial supercooling and monotonically growing hadronic bubbles.
