Single cluster catalysts (SCCs), which exhibit remarkable catalytic performance due to their high metal loading and synergy effect between metal atoms, have attracted great attention in research. Herein, by means of density functional theory calculations, the oxygen reduction reaction (ORR), oxygen evolution reaction (OER), and hydrogen evolution reaction (HER) performances of precious metal (Pt, Pd, Rh, and Ir) trimetallic single-cluster electrocatalyst (U_xV_yW_z-NG) are investigated. The calculation results show that Pt, Pd, and Ir have significant effect on ORR, OER, and HER, respectively, and all the calculated U_xV_yW_z-NG structures are thermodynamically stable due to the negative formation energies and binding energies. The Pt₃-NG, Pd₃-NG, and Ir₃-NG show the lowest ORR, OER, and HER overpotentials of 0.63, 0.77, and −0.02 V, respectively, among all combinations of U_xV_yW_z-NG. These overpotentials are lower than that of precious metal single atom catalysts (SACs), which indicate better activities of precious trimetallic SCCs than those of SACs. The electronic structure reveals that the O-2p orbital shows strong hybridization strength with Pt-3d orbitals in the system of OH adsorbed Pt₃-NG and thus facilitates the electrocatalytic reactions. The results are helpful for the rational design of high-performance triatomic catalysts.