Transition metal single-atom catalysts have attracted great attention because of their great potential applications in the chemical industry. Except for graphene, there are few single-layer materials that can act as substrates to support the dispersive metal atoms. Recently, a biphenylene layer, a new two-dimensional allotrope of graphene, was synthesized in experiments, providing a new substrate layer to fabricate single-atom catalysts (SACs). In this work, we predict three transition metal SACs MN4-biphenylene (M = Fe, Co, and Ni) based on first-principles calculations. The results indicate that FeN4-biphenylene is a promising bifunctional catalyst with low overpotentials for both the oxygen reduction reaction and oxygen evolution reaction, ηORR = 0.11 V and ηOER = 0.27 V. The high catalytic activities are explained by the position of the d-band center of the Fe atom in the biphenylene network and the strength of interaction between FeN4-biphenylene and the reaction intermediates.