Rationally designing efficient, low-cost and stable catalysts toward the oxygen evolution reaction (OER) and the oxygen reduction reaction (ORR) is of significant importance to the development of renewable energy technologies. In this work, we have systematically investigated a series of potentially efficient and stable single late transition metal atom doped phthalocyanines (TM@Pcs, TM = Mn, Fe, Co, Ni, Cu, Ru, Rh, Pd, Ir and Pt) as single-atom catalysts (SACs) for applications toward the OER and ORR through a computational screening approach. Our calculations indicate that TM atoms can tightly bind with Pc monolayers with high diffusion energy barriers to prevent the isolated atoms from clustering. The interaction strength between intermediates and TM@Pc governs the catalytic activities for the OER and ORR. Among all the considered TM@Pc catalysts, Ir@Pc and Rh@Pc were found to be efficient OER electrocatalysts with overpotentials ηOER of 0.41 and 0.44 V, respectively, and for the ORR, Rh@Pc exhibits the lowest overpotential ηORR of 0.44 V followed by Ir@Pc (0.55 V), suggesting that Rh@Pc is an efficient bifunctional catalyst for both the OER and ORR. Moreover, it is worth noting that the Rh@Pc catalyst can remain stable against dissolution under the pH = 0 condition. Ab initio molecular dynamic calculations suggest that Rh@Pc could remain stable at 300 K. Our findings highlight a novel family of two-dimensional (2D) materials as efficient and stable SACs and offer a new strategy for catalyst design.