The structure and properties of the new (Al,Cu)4Ca, Al27Ca3Cu7, and Al8CaCu4 intermetallic compounds in equilibrium with aluminum solid solution in the ternary Al–Ca–Cu alloying system were comprehensively analyzed. The (Al,Cu)4Ca intermetallic compound is treated as a line phase based on the Al4Ca phase with Cu substituted by Al. The solubility of copper in the compound reaches 10 at.% (19 wt.%), which leads to marked changes in the crystal lattice structure, physical and mechanical properties of the compound. For instance, the density of the compound increases from 2.22 to 2.79 g/cm3 and the microhardness from HV 180 to HV 250. The Al27Ca3Cu7 phase is treated as a strict stoichiometric ternary compound with a primitive BaHg11 type crystal structure of the Pm3m space group. The lattice parameter is accepted to be 8.514 Å corresponding to a density of 3.45 g/cm3. The Al8CaCu4 phase is also a strict stoichiometric ternary compound with a tetragonal crystal lattice structure of the Mn12Th type. The phase has the highest microhardness (HV 505) and density (4.57 g/cm3). The alloys pertaining to the binary (Al)+(Al,Cu)4Ca phase field and the quasi-binary (Al)+Al27Ca3Cu7 section can be considered promising as the base for new natural aluminum matrix composites.