Layered two-dimensional (2D) conjugated metal-organic frameworks (MOFs) represent a family of rising electrocatalysts for the oxygen reduction reaction (ORR), due to the controllable architectures, excellent electrical conductivity, and highly exposed well-defined molecular active sites. Herein, we report a copper phthalocyanine based 2D conjugated MOF with square-planar cobalt bis(dihydroxy) complexes (Co-O4 ) as linkages (PcCu-O8 -Co) and layer-stacked structures prepared via solvothermal synthesis. PcCu-O8 -Co 2D MOF mixed with carbon nanotubes exhibits excellent electrocatalytic ORR activity (E1/2 =0.83 V vs. RHE, n=3.93, and jL =5.3 mA cm-2 ) in alkaline media, which is the record value among the reported intrinsic MOF electrocatalysts. Supported by in situ Raman spectro-electrochemistry and theoretical modeling as well as contrast catalytic tests, we identified the cobalt nodes as ORR active sites. Furthermore, when employed as a cathode electrocatalyst for zinc-air batteries, PcCu-O8 -Co delivers a maximum power density of 94 mW cm-2 , outperforming the state-of-the-art Pt/C electrocatalysts (78.3 mW cm-2 ).