In　this　paper,　we　construct　all　the　indecomposable　modules　of　a　class　of　non-pointed　Hopf　algebras,　which　are　quotient　Hopf　algebras　of　a　class　of　prime　Hopf　algebras　of　GK-dimension　one.　Then　the　decomposition　formulas　of　the　tensor　product　of　any　two　indecomposable　modules　are　established.　Based　on　these　results,　the　representation　ring　of　the　Hopf　algebras　is　characterized　by　generators　and　some　relations.