The development of highly-efficient catalysts for oxygen reduction reaction (ORR) or oxygen evolution reaction (OER) is highly crucial for the commercial applications of some novel energy-related devices. Herein, using comprehensive first-principles computations, the potential of a variety of single metal-based catalysts supported by MoSe2 nanosheet to boost the ORR or OER process was evaluated. The computations revealed that these considered metal atoms can be more stably anchored on 1 T-MoSe2 than those of on 2H-MoSe2. In particular, the supported Ni and Pd catalysts on 1 T-MoSe2 exhibit high OER activity due to their quite low overpotential (0.47 and 0.49 V). Meanwhile, the anchored Pd atom on 1 T-MoSe2 also displays excellent ORR performance with an ultra-low overpotential of 0.32 V, thus implying its superior bifunctional activity for ORR/OER. Our results provide a quite promising avenue to design a new class of MoSe2-based single atom catalysts for fuel cells, which also further enriches the application fields of MoSe2 nanosheets in advanced catalysis.