Two-dimensional (2D) materials confining single atoms (SAs) for catalysis, such as graphene confining metal single atoms (M-N-C), integrate both aspects of 2D materials and single-atom catalysts (SACs). Significant advantages have been established in this new category of catalysts, which have seen rapid development in recent years. Recent studies have suggested a new class of novel 2D materials with a chemical formula of MN4 naturally holding a uniformly distributed M-N4 moiety. We investigated MN4 monolayers as multifunctional catalysts for the hydrogen-evolution reaction (HER), oxygen-evolution reaction (OER), and oxygen-reduction reaction (ORR). Among them, the IrN4 monolayer demonstrated high catalytic activity towards these three reactions. The CoN4 monolayer was predicted to be an excellent bifunctional catalyst for the OER and ORR. A uniformly distributed and short-distanced M-N4 moiety on the MN4 monolayer made reactions between the intermediates during the OER and ORR possible, facilitating the release of O2 and H2O, respectively. In addition, the M atom of the MN4 monolayer having electronic states located at the Fermi level was active for catalyzing the HER. More importantly, changes in the Gibbs free energy of the two key intermediates of adsorption (ΔGOH* and ΔGOOH*) correlated closely with the Bader charge on the M atom (BM).