Let　G　=　(V,　E)　be　a　graph.　The　atom-bond　connectivity　(ABC)　index　is　defined　as　the　sum　of　weights　((d(u)　+　d(v)　-　2)/d(u)d(v))(1/2)　over　all　edges　uv　of　G,　where　d(u)　denotes　the　degree　of　a　vertex　u　of　G.　In　this　paper,　we　give　the　atom-bond　connectivity　index　of　the　zigzag　chain　polyomino　graphs.　Meanwhile,　we　obtain　the　sharp　upper　bound　on　the　atom-bond　connectivity　index　of　catacondensed　polyomino　graphs　with　h　squares　and　determine　the　corresponding　extremal　graphs.