Metal-based alloys encapsulated in nitrogen-doped carbon (alloy@NC) catalysts with high-efficiency and cost-effective are promising to solve the sluggish kinetics of the oxygen reduction/oxygen evolution reaction (ORR/OER) in Zn-air batteries (ZABs). Here, a novel FeNi₃ alloy nanoparticles encapsulated by N-doped carbon graphene nanotubes (FeNi₃@NC) catalyst with 0D/1D/3D multi-structure is synthesized through combining ligand-assisted and in-situ catalytic assembly strategy. The hybrid catalyst FeNi₃@NC exhibited highly efficient ORR catalytic activity and stability. Impressively, the FeNi₃@NC only required an overpotential of 291 mV to drive a current density of 10 mA cm^-2, successfully demonstrating their excellent bifunctional catalytic activity. Moreover, the assembled rechargeable Zn-air battery based on FeNi₃@NC air electrode exhibited high power density of 149.7 mW cm^-2 and specific capacity of 658 mAh g_Zn^-1, and long-term stability up to 280 hours, outperforming most of the recently reported catalysts. Density functional theory (DFT) reveals that C atom adjacent to the pyridinic-N in FeNi₃@NC act as the active sites for ORR/OER, since the alloying FeNi₃ combined by pyridinic-N effectively break electroneutrality of the C atom, thereby accelerating the kinetics process of the ORR/OER. This work provides some constructive guidelines for fabricating alloy@NC catalysts with bifunctional catalytic activity and deeply demonstrates the applicability modulate the electronic configuration to construct high-performance rechargeable ZABs.