The materials of the Al-Ni-Ce ternary system have promising application potential in additive manufacturing, and the systematic study of Al-Ni-Ce IMCs is an important part of the design and performance development of Al-Ni-Ce alloys. In this paper, the mechanical properties and electronic properties of seven major Al-Ni-Ce IMCs are studied using first-principles calculations, and the differences in their mechanical properties are discussed. The enthalpy of formation and cohesion energy of the Al-Ni-Ce IMCs showed that Ce4Al23Ni6 had the highest enthalpy of formation and cohesion energy, which were −49.57 kJ/mol and −4.47 kJ/mol, respectively. This demonstrated that all Al-Ni-Ce IMCs had excellent thermodynamic stability. The elastic modulus calculation of the Al-Ni-Ce IMCs showed that the Young’s modulus of CeAl3Ni2 was the largest at 178.15 GPa, the bulk modulus of CeAlNi4 was the largest at 125.78 GPa, and the shear modulus of CeAlNi2 was the largest at 62.53 GPa. This proved that among the Al-Ni-Ce IMCs, CeAl3Ni2 had the greatest stiffness, CeAlNi4 had the strongest resistance to uniform deformation, and CeAl3Ni2 had the strongest resistance to plastic deformation. The electronic density of states of Al-Ni-Ce IMCs was analyzed, and the results showed that the main bonding types of Al-Ni-Ce IMCs were metallic and covalent bonds. This work can provide a theoretical basis for the material design and development of the Al-Ni-Ce ternary system.