Trifunctional ORR/OER/HER catalysts are emerging for various sustainable energy storage and conversion technologies. For this function, employing materials with 1D structures leads to catalysts having limited surface area and structural robustness. Instead of 1D catalysts, heterostructured catalysts (i.e., catalysts consisting of interfaces created by combining diverse structural components) have attracted much attention due to their high efficiency. We have fabricated a directly grown 1D-1D heterostructured bimetallic N-doped carbon trifunctional catalyst based on Fe/Co bimetallic-organic frameworks, forming nanobrushes (FeCoNC-NB) with improved resistance to collapsing and substantial numbers of exposed active sites. The secondary 1D structure of this design contributes to creating interparticle conductive networks. By combining the brush-like heterostructure, FeCo alloy active sites, and N-doped carbon as support and for encapsulation of the metal, the catalyst features a high ORR Eonset value (1.046 V), low OER overpotential (363 mV), and comparable HER overpotential (254 mV) in alkaline electrolyte. Zn-air batteries with FeCoNC-NB demonstrate a power density of 195 mW cm-2 and a superior battery life of up to 350 h. Self-powered FeCoNC-NB-based water electrolyzers as energy conversion devices are also demonstrated. This work drives the progress of trifunctional catalysts based on heterostructured nonprecious metal N-doped carbon for energy storage and conversion developments.