In　this　paper,　we　mainly　focus　on　the　unique　normal　form　for　a　class　of　three-dimensional　vector　fields　via　the　method　of　transformation　with　parameters.　A　general　explicit　recursive　formula　is　derived　to　compute　the　higher　order　normal　form　and　the　associated　coefficients,　which　can　be　achieved　easily　by　symbolic　calculations.　To　illustrate　the　efficiency　of　the　approach,　a　comparison　of　our　result　with　others　is　also　presented.