Two hybrid compounds, namely [Cu(3atrz)4][PMoMoVO40] (1) and [Cu(3atrz)6][PMo12O40]2 (2), were synthesized through hydrothermal reactions of 3-amino-1,2,4-triazole (3atrz), phosphomolybdic acid (PMA) and appropriate copper salts. Crystal structure analysis reveals that compound 1 contains one-dimensional Cu-3atrz chains. The unit of compound 2 contains a double calyx[3]arene-shaped hexamer, which is composed of six two-coordinated CuI atoms and six 3atrz ligands. Both compounds 1 and 2 present a three-dimensional hybrid structure, which is built by the self-assembly of Cu-3atrz clusters and Keggin-type PMA units. The resulting hybrid compounds can act as highly efficient heterogeneous catalysts for the selective oxidation of olefins with molecular oxygen as the oxidant in the presence of a trace amount of tert-butyl hydroperoxide (t-BuOOH). Their excellent catalytic properties can be mainly attributed to the existence of stabilized CuI complexes with an appropriate chemical environment and a spacious structure, which can interact with t-BuOOH to form catalytic sites for the direct activation of O2. This work demonstrates that the hybrid compounds assembled from copper-3atrz complexes and phosphomolybdic acid may have great potential in molecular O2-mediated catalytic oxidation reactions, which can certainly build a platform for deep insight into the biologically relevant catalytic oxidation processes.