The stability of an Einstein static universe in the DGP braneworld scenario is studied in this letter .
Two separate branches denoted by \epsilon = \pm 1 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 < - \frac { 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 .