To　research　hypernormal　form　(simplest　normal　form,　unique　normal　form)　of　nilpotent　three-dimensional　vector　fields,　the　problem　of　quintic　hypernormal　form　of　a　class　of　nilpotent　three-dimensional　vector　fields　with　symmetrical　property　was　studied　by　using　new　grading　function　and　the　method　of　multiple　Lie　brackets　and　by　introducing　the　new　marks　for　block　matrices　firstly,　then　that　the　second　order　normal　form　of　above　vector　field　was　hypernormal　form　had　been　proved,　and　the　unique　form　of　the　second　order　quintic　hypernormal　form　was　obtained.　At　last,　the　degenerate　case　of　above　vector　fields　was　studied,　and　that　this　could　be　consistent　with　the　conclusions　in　dimension　2　was　verified.