  In the standard picture of cosmology it is predicted that a phase transition,
associated with chiral symmetry breaking after the electroweak transition, has
occurred at approximately 10 \mu seconds after the Big Bang to convert a plasma
of free quarks and gluons into hadrons. We consider the quark-hadron phase
transition in a DGP brane world scenario within an effective model of QCD. We
study the evolution of the physical quantities useful for the study of the
early universe, namely, the energy density, temperature and the scale factor
before, during, and after the phase transition. Also, due to the high energy
density in the early universe, we consider the quadratic energy density term
that appears in the Friedmann equation. In DGP brane models such a term
corresponds to the negative branch (\epsilon=-1) of the Friedmann equation when
the Hubble radius is much smaller than the crossover length in 4D and 5D
regimes. We show that for different values of the cosmological constant on a
brane, \lambda, phase transition occurs and results in decreasing the effective
temperature of the quark-gluon plasma and of the hadronic fluid. We then
consider the quark-hadron transition in the smooth crossover regime at high and
low temperatures and show that such a transition occurs along with decreasing
the effective temperature of the quark-gluon plasma during the process of the
phase transition.
