Exploring highly efficient bifunctional electrocatalysts toward the oxygen reduction and evolution reactions is essential for the realization of high-performance rechargeable zinc-air batteries. Herein, a novel nanofibrous bifunctional electrocatalyst film, consisting of metallic manganese sulfide and cobalt encapsulated by nitrogen-doped carbon nanofibers (CMS/NCNF), is prepared through a continuous electrospinning method followed by carbonization treatment. The CMS/NCNF bifunctional catalyst shows both comparable ORR and OER performances to those of commercial precious metal-based catalysts. Furthermore, the free-standing CMS/NCNF fibrous thin film is directly used as the air electrode in a solid-state zinc-air battery, which exhibits superior flexibility while retaining stable battery performance at different bending angles. This study provides a versatile design route for the rational design of free-standing bifunctional catalysts for direct use as the air electrode in rechargeable zinc-air batteries.