The development of bifunctional single-atom catalysts (SACs) for overall water splitting is crucial for clean energy production in the context of sustainable development. Using first-principles calculations, the catalytic capability of different transition metal (TM) atoms supported on biphenylene (Bip) monolayers (TM@Bip, TM = V-Cu, Ru-Ag, and Ir-Au) is comprehensively investigated. Bip can directly anchor TM atoms without engineered vacancies or nitrogen defects. Among the screened SACs, Pd@Bip is found to be an excellent bifunctional catalyst for both the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER). The overpotentials for the HER and the OER were calculated to be 0.05 and 0.50 V, respectively, which are even superior to the commercialized catalysts like Pt and IrO2. Furthermore, adjusting the d-band center of TM atoms effectively modulates the catalytic activity, and the optimal OER performance of TM-Bip can be achieved with a d-band center of -2.32 eV, which can serve as a principle to design Bip-based SACs. Our findings may serve as a practical theoretical guide for the exploration of effective bifunctional SACs for overall water splitting.