  Our main aim in this paper is to investigate the rigidity of complete
noncompact gradient steady Ricci solitons with harmonic Weyl tensor. More
precisely, we prove that an $n$-dimensional ($n\geq 5$) complete noncompact
gradient steady Ricci soliton with harmonic Weyl tensor and multiply warped
product metric is either Ricci flat or isometric to the Bryant soliton up to
scaling. Meanwhile, for $n\ge 5$, we provide a local structure theorem for
$n$-dimensional connected (not necessarily complete) gradient Ricci solitons
with harmonic Weyl curvature and multiply warped product metric.
