We　construct　a　weak　Hopf　algebra　(SIC)　X-q(A(1))　corresponding　to　non-standard　quantum　group　X-q(A(1)).　The　PBW　basis　of　(SIC)　X-q　(A(1))　is　described　and　all　the　highest　weight　modules　of　(SIC)　X-q(A(1))　are　classified.　Finally　we　give　the　Clebsch-Gordan　decomposition　of　the　tensor　product　of　two　highest　weight　modules　of　(SIC)　X-q(A(1)).