There　are　lots　of　methods　for　complete　independence　test　for　high-dimensional　random　vector.　However,　it　is　difficult　for　practitioners　to　choose　a　powerful　test　because　the　true　alternative　hypothesis　is　unknown.　Combining　the　L-2-type　with　the　L-infinity-type　test　statistic,　we　propose　a　rank-based　test　method.　From　a　technical　point　of　view,　the　proposed　test　is　distribution-free　and　consequently　the　corresponding　critical　values　or　p-values　can　be　obtained　by　Monte　Carlo　methods.　Compared　with　permutation　or　bootstrap　test　methods,　the　proposed　test　method　saves　calculation　cost.　Simulation　results　show　that　the　resulting　method　has　excellent　performance　with　finite　sample　size.　We　also　provide　a　real　data　application　to　demonstrate　the　practicality　and　effectiveness　of　the　proposed　test　method.