  We study the long time behavior of the volume preserving $p$-flow in
$\mathbb{R}^{n+1}$ for $1\leq p<\frac{n+1}{n-1}$. By extending Andrews'
technique for the flow along the affine normal, we prove that every centrally
symmetric solution to the volume preserving $p$-flow converges sequentially to
the unit ball in the $C^{\infty}$ topology, modulo the group of special linear
transformations.
