  In the paper, we analysis the asymptotic behavior of noncompact
$\kappa$-noncollapsed steady gradient Ricci soliton $(M, g)$ with nonnegative
curvature operator away from a compact set $K$ of $M$. In particular, we prove:
any $4d$ noncompact $\kappa$-noncollapsed steady gradient Ricci soliton $(M^4,
g)$ with nonnegative sectional curvature must be a Bryant Ricci soliton up to
scaling if it admits a sequence of rescaled flows of $(M^4, g)$, which
converges subsequently to a family of shrinking quotient cylinders.
