Sluggish kinetics of oxygen reduction reaction (ORR) on air-cathode of microbial fuel cells (AC-MFCs) is one of the main obstacles for energy loss. In this study, nitrogen-doped Fe3Se4/FeSe/partially-graphitized carbon (Fe3Se4/FeSe/NPGC) composites as non-precious-metal air-cathode (ORR) catalysts are obtained using waste biomass (cornstalk cores) as raw material. As carbonization temperature increases (800-950 degrees C), the crystalline phase transition between Fe3Se4 and FeSe is strengthened to form the Fe3Se4/FeSe heterojunctions. The highest power density (1003 mW m(-2)) and durability (decline of 7.8% after 105 d operation) are obtained by Fe3Se4/FeSe/NPGC (850 degrees C) cathode in AC-MFCs, which are higher than those of Pt/C (840 mW m(-2), 52.4%). The high ORR activity of Fe3Se4/FeSe/NPGC (850 degrees C) is partly attributed to the large specific surface area (356.68 m(2) g(-1)) and porous structure. Doped N atoms (pyridinic N, pyrrolic N and graphitic N) in carbon skeleton enhance the charge delocalization of C atoms to reduce the electron loss to enhance the electron utilization via a four-electron (4e(-)) ORR pathway. Fe3Se4/FeSe heterojunctions should greatly promote the charge transfer and oxygen dissociation efficiencies. The highly-conductive NPGC skeleton also contributes to the efficient charge transfer. The good long-term durability of AC-MFCs with Fe3Se4/FeSe/NPGC (850 degrees C) cathode is mainly ascribed to its fast ORR kinetics, which still generates a small amount (below 10.0%) of H2O2 ((OH)-O-center dot and O-center dot(2)-) intermediate to inhibit the electrogenic microbe growth on cathode surface. This work not only provides the fundamental studies on carbon-supported transition-metal selenides for ORR, but also provides a new kind of promising alternatives for precious metal-based electrodes for AC-MFCs.