  In this paper we consider a $Z_2$ symmetrical 3-brane embedded in a
5-dimensional spacetime. We study the effective Einstein equation and
acceleration condition in presence of the quintom dark energy fluid as the bulk
matter field. It is shown that the time-dependent bulk quintom field induces a
time-dependent cosmological constant on the brane. In the framework of the DGP
model, the effective Einstein equation is obtained in two different cases: i)
where the quintom field is considered as the bulk matter field and the brane is
empty and, ii) where the quintom dark energy is confined on the brane and the
bulk is empty. We show that in both cases one could obtain a self-inflationary
solution at late time in positive branch $\epsilon=1$, and an asymptotically
static universe in negative branch $\epsilon=-1$.
