  The stability of an Einstein static universe in the DGP braneworld scenario
is studied in this paper. Two separate branches denoted by $\epsilon=\pm1$ of
the DGP model are analyzed. Assuming the existence of a perfect fluid with a
constant equation of state, $w$, in the universe, we find that, for the branch
with $\epsilon=1$, there is no a stable Einstein static solution, while, for
the case with $\epsilon=-1$, the Einstein static universe exists and it is
stable when $-1<w<-1/3$. Thus, the universe can stay at this stable state
past-eternally and may undergo a series of infinite, non-singular oscillations.
Therefore, the big bang singularity problem in the standard cosmological model
can be resolved.
