Single-atom catalysts (SACs) have provoked significant curiosity in heterogeneous catalysis due to the benefits of maximum metal atoms usage, robust metal-support interaction, single-metal-atom active sites, and high catalytic efficiency. Transition metal (M1) adatoms anchored on highly stable phosphotungstic acid (PTA) cluster (Scheme 1) provide an opportunity for altering their electronic, magnetic and catalytic characteristics. In this study, the electronic structures and catalytic mechanism of ethyne hydrogenation of SACs with the group-9 metal atoms M1 (M1= Co, Rh, Ir) anchored on PTA cluster have been explored by using first-principles quantum calculations. It is found that the catalytic activity of ethyne hydrogenation is determined by two critical parameters: the adsorption energies of the adsorbate (H2, C2H2) and the activation energy barrier of ethyne hydrogenation. We have shown that the reaction pathway of ethyne hydrogenation reaction on the experimentally characterized Rh1/PTA at room temperature consists of three steps: C2H2 and H2 coadsorption on Rh1/PTA, H2 attacking C2H2 to form C2H4, then C2H4 desorbing or further reacting with H2 to produce C2H6 and completing the catalytic cycle. The Rh1/PTA possesses fair catalytic activity with C2H4 desorption energy of 1.46 eV at the rate determining step and high selectivity for ethylene formation through the Langmuir−Hinshelwood mechanism. The potentially competitive mechanism for the formation of ethane is not kinetically favorable, with a 2.59 eV barrier for ethylene hydrogenation. Moreover, micro-kinetics analysis is also carried out to further understand the mechanism and catalytic performance. The work reveals that the PTA supported SACs can be a promising catalyst for alkyne hydrogenation.