Searching for highly efficient and cost-effective bifunctional electrocatalysts for the oxygen evolution reaction (OER), oxygen reduction reaction (ORR) and hydrogen evolution reaction (HER), which can be applied to water splitting, fuel cells and metal-air batteries, is critical for developing clean and renewable energies. Yet it remains a great challenge. By means of first-principles calculations, we have studied the OER, ORR and HER catalytic activity of Mo2B2 MBene-supported single-atom catalysts (SACs) by embedding a series of transition metal atoms in the Mo vacancy (TM@Mo2B2, TM = Ti, V, Cr, Mn, Fe, Co, Ni and Cu) as electrocatalysts. All TM@Mo2B2 SACs show excellent metallic conductivity, which would be favorable for the charge transfer in electrocatalytic reactions. Importantly, Ni@Mo2B2 can be used as a HER/OER bifunctional electrocatalyst with a lower vertical bar Delta G(H)vertical bar (-0.09 eV) for the HER under 1/4H coverage and a lower overpotential (eta(OER) = 0.52 V) than that of IrO2 (eta(OER) = 0.56 V) for the OER, while Cu@Mo2B2 can be used as an OER/ORR bifunctional electrocatalyst with a lower overpotential (eta(OER) = 0.31 V) than that of IrO2 (eta(OER) = 0.56 V) and RuO2 (eta(OER) = 0.42 V) for the OER and a lower overpotential of 0.34 V than that of Pt (eta(ORR) = 0.45 V) for the ORR, for both of which the transition metal atoms serve as the active sites. This work could open up an avenue for the development of non-noble-metal-based bifunctional MBene electrocatalysts.