Developing highly active and durable non-noble metal based bifunctional electrocatalysts is still a key step for rechargeable metal-air batteries. In the current work, a new three-dimensional cyanide-bridged CoNi complex {{[Ni(pn)2]3[Co(CN)6]2}·3H2O}n (pn = 1, 3-diaminopropane) was synthesized and characterized. And a bifunctional electrocatalyst CoNi@GO for both oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) was prepared by pyrolyzing process with graphene oxide (GO) as template and CoNi complex as precursor. Density functional theory calculations revealed that the nanostructured CoNi alloy embedded in the lamellar porous GO and there was strong synergistic coupling between the carbon based material and CoNi alloy. The as-obtained catalyst showed the outstanding electrocatalytic activity and the excellent potential difference between ORR and OER is 0.697 V versus Pt/C+RuO2 (0.708 V). The Zinc-air battery prepared with CoNi@GO as an air electrode has a small charge-discharge voltage gap of 0.91 V, a high energy efficiency of 59.5%, and could be cycled stably for more than 240 h at 10 mA cm−2. This work confirmed the feasibility of developing coordination polymer (CP) based non-noble metal bi-functional electrocatalysts for energy storage and conversion, and provided a valuable strategy for the rational design of new non-noble metal electrocatalysts in future.