In　this　paper,　the　higher　order　asymptotic　expansion　of　the　moments　of　extreme　from　generalized　Maxwell　distribution　is　gained,　by　which　one　establishes　the　rate　of　convergence　of　the　moment　of　the　normalized　partial　maximum　to　the　moment　of　the　associated　Gumbel　extreme　value　distribution.