The structure and properties of CaF2-type δ structure of helium-containing zirconium hydrides were investigated using density functional theory. The properties of this material vary with hydrogen and helium concentrations. Hydrogen has a significant effect on the behavior of helium. The occupied sites of He atoms strongly depend on the hydrogen concentration. The structures and formation mechanisms of helium clusters vary with hydrogen concentration at a high helium content. The embedding energies of He atoms mainly result from interactions between helium and zirconium atoms. However, H-He interactions significantly contribute to the embedding energies. Variations in lattice volume expansion and bulk modulus were also investigated.