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In the paper, we analysis the asymptotic behavior of noncompact$\kappa$-noncollapsed steady gradient Ricci soliton $(M, g)$ with nonnegativecurvature 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 toscaling if it admits a sequence of rescaled flows of $(M^4, g)$, whichconverges subsequently to a family of shrinking quotient cylinders.

$4d$ steady gradient Ricci solitons with nonnegative curvature away from a compact set