LetX,X1,X2,···beasequenceofnondegeneratei.i.d.randomvariableswithzeromeans,whichisinthedomainofattractionofthenormallaw.Let{ani,1≤i≤n,n≥1}beanarrayofrealnumberswithsomesuitableconditions.Inthispaper,weshowthatacentrallimittheoremforself-normalizedweightedsumsholds.WealsodeduceaversionofASCLTforself-normalizedweightedsums.