A high-performance one-dimensional (1D) nanofibrillar N-Co-C oxygen reduction reaction (ORR) catalyst was fabricated via electrospinning using renewable natural alginate and multiwalled carbon nanotubes (MWCNTs) as precursors, where Co nanoparticles (NPs) are encapsulated by nitrogen (N)-doped amorphous carbon and assembled on MWCNTs. The 1D morphology not only prevents the aggregation of the Co NPs, but also provides a typical multimodal mesoporous structure which is beneficial for the O-2 diffusion and the migration of adsorbed superoxide. In combination with the high conductivity of CNTs, the N-doped amorphous carbon shell can exert electron release on the encapsulated Co NPs, and thus enhance the ORR activity. It is also a protective layer that stabilizes the Co NPs, which ensures a high ORR activity of the catalysts in both alkaline and acid media and long-term durability. So compared with a commercial Pt/C catalyst, as expected, the N-Co-C nanofiber reported herein exhibited a comparable current density and onset potential (-0.06 V), with better durability in alkaline and acid solutions and better resistance to crossover effects in the ORR.