The　aim　of　this　paper　is　to　describe　all　PBW-deformations　of　the　connected　graded　K-algebra　A　generated　by　x(i),1　＜=　i　＜=　n,　with　the　braiding　relations:　{x(i)(2)　=　0,　1　＜=　i　＜=　n,　x(i)x(j)　=　x(j)x(i),|　j　-　i|　＞　1,　x(i)x(i)+1x(i)　=　x(i)+1x(i)x(i+1),1　＜=　i　＜=　n　-　1　Firstly,　the　complexity　C(A)　of　the　algebra　A　is　computed.　Then　all　PBW-deformations　of　A　when　n　＞=　2　are　given　explicitly　with　the　help　of　the　general　PBW-deformation　theory　introduced　by　Cassidy　and　Shelton.　Finally,　it　is　shown　that　each　non-trivial　PBW-deformation　of　A　is　isomorphic　to　a　Iwahori-Hecke　algebra　Hq(n+1)　(of　type　A)　with　n　generators　and　an　appropriate　parameter　q.　Here,　trivial　PBW-deformations　of　A　mean　that　those　PBW-deformations　that　are　isomorphic　to　A.