Quasicrystals and approximant crystals (ACs) have a unique complex structure with many crystallographically non-equivalent sites. In order to apply this characteristic potential to catalysts, we investigated catalytic properties of Pd-containing Tsai-type 1/1 ACs, i.e., Al-Pd-Sc and Ga-Pd-Sc, in the acetylene hydrogenation reaction and also performed density functional theory calculations of adsorption energies of reactants and products. The catalytic properties are found to significantly depend on the kind of the semimetal element such as Al and Ga, where the Al-Pd-Sc 1/1 AC shows higher catalytic activity and selectivity. The adsorption energy of reactant acetylene is smaller in the Al-Pd-Sc 1/1 AC whereas the amount of product ethylene are comparable for both ACs. Therefore, the adsorption rate of reactants is increased while the desorption rate of products remains almost the same in the Al-Pd-Sc 1/1 AC. Furthermore, the adsorption energies are found to differ significantly from site to site, implying a superior potential of ACs for designation of active sites using many non-equivalent crystallographic sites for high catalytic performance.