The　aim　of　this　paper　is　to　classify　all　Hopf　algebra　structures　on　the　quotient　of　Ore　extensions　H-4[z;sigma]of　automorphism　type　for　the　Sweedler　＇　s　4-dimensional　Hopf　algebra　H-4.　Firstly,　we　calculate　all　equivalent　classes　of　twisted　homomorphisms　(sigma,J)　for　H-4.　Then　we　give　the　classification　of　all　bialgebra　(Hopf　algebra)　structures　on　the　quotients　of　H-4[z;sigma]　up　to　isomorphism.