  In this paper, we proved that any 2-convex solution $u$ of $\sigma_2(D^2u)=1$
with a quadratic growth must be a quadratic polynomial in $\mathbb{R}^n\ (n\geq
3 )$ by using a Pogorelov estimate and the global gradient estimate. And we
give a positive answer to the unresolved issue in \cite{CX}.
