To address the urgent need for accurate hydrogen leakage detection during storage and transportation and overcome the limitations of conventional gas-sensing materials, such as low sensitivity and poor selectivity, we systematically investigate the structural characteristics, electronic properties, and hydrogen sensing performance of biphenylene nanoribbon (BPNN) using first-principles calculations combined with density functional theory and the nonequilibrium Green’s function approach. Through comprehensive screening of different edge-passivation configurations, oxygen-passivated armchair BPNNs are identified to simultaneously achieve excellent structural stability and metallic conductivity. However, pristine O-passivated BPNNs exhibit weak interactions with H₂, with adsorption energies below 0.01 eV, indicating typical van der Waals-dominated physisorption and limited sensing capability. To enhance the hydrogen sensing performance, transition-metal Co atom is introduced onto the BPNN surface to construct highly active adsorption sites. The results demonstrate that Co functionalization significantly strengthens the interaction between H₂ molecules and the substrate, leading to chemisorption with adsorption energies exceeding 1 eV. Moreover, each Co-decorated BPNN configuration can stably accommodate up to two H₂ molecules. Furthermore, quantum transport calculations reveal pronounced anisotropic sensing characteristics in BPNN-Co-based devices. The armchair BPNN-Co devices exhibit substantially higher sensitivity toward H₂ concentration variations than their zigzag counterparts while maintaining excellent selectivity in the presence of O₂, N₂, and H₂O. Notably, O₂ further enhances the sensing response, achieving a maximum sensitivity of 36.12%, whereas N₂ and H₂O introduce negligible interference. Although zigzag BPNN-Co devices possess higher electrical conductivity, their sensing responses toward H₂ adsorption and environmental changes remain limited. Overall, Co-decorated biphenylene nanoribbons represent a promising platform for hydrogen sensing, particularly for low-concentration H₂ leak detection, and provide valuable theoretical insights into the rational design of high-performance hydrogen sensors.