This　paper　concerns　with　efficient　projection　onto　the　ordered　weighted　ℓ1　norm　ball,　which　is　equivalent　to　the　problem　of　finding　projector　onto　the　intersection　of　the　monotone　nonnegative　cone　and　an　affine　subspace.　Based　on　Lagrangian　relaxation　and　secant　approximation　method,　we　propose　an　easily　implementable　yet　efficient　algorithm　to　solve　the　projection　problem　which　is　proved　to　terminate　after　a　finite　number　of　iterations.　Furthermore,　we　design　efficient　implementations　for　our　algorithm　and　compare　it　with　a　semismooth　Newton　(Ssn)　algorithm　and　a　root-finding　(Root-F)　algorithm.　Numerical　results　on　a　diversity　of　test　problems　show　that　our　algorithm　is　superior　than　Ssn　and　Root-F.　©　2022,　Operations　Research　Society　of　China,　Periodicals　Agency　of　Shanghai　University,　Science　Press,　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.