Non-central　chi-squared　distribution　plays　a　vital　role　in　commonly　used　statistical　testing　procedures.　The　non-centrality　parameter　A　provides　valuable　information　on　the　power　of　the　associated　test.　In　this　paper.　based　on　one　observation　X　sampled　from　a　chi-squared　distribution　with　p　degrees　of　freedom　and　non-centrality　parameter　S,　we　study　a　new　class　of　non-centrality　parameter　estimators　(delta)　over　cap　(beta)(X)　=　max　{X　-　p.　beta　X),　0　＜=　beta　＜　1,　and　investigate　their　statistical　properties　under　the　quadratic　loss　function.　Theoretical　and　simulation　studies　indicate　that　＜(delta)over　cap＞(1/(1+p))(X)　generally　works　well　compared　with　other　existing　estimators,　especially　for　relatively　small　and　moderate　delta.　(c)　2008　Elsevier　B.V.　All　rights　reserved.