Based on the first principles, the structural stability, mechanical characteristics, electronic structure, and thermodynamic properties of AlCu2M (M = Ti, Cr, Zr, Sc, Hf, Mn, Pa, Lu, Pm) are investigated. The calculated results indicate that the AlCu2Pa crystal structure is more stable and that AlCu2Pa should be easier to form. All of the AlCu2M compounds have structural stability in the ground state. Elastic constants are used to characterize the mechanical stability and elastic modulus, while the B/G values and Poisson ratio demonstrate the brittleness and ductility of AlCu2M compounds. It is demonstrated that all computed AlCu2M compounds are ductile and mechanically stable, with AlCu2Hf having the highest bulk modulus and AlCu2Mn having the highest Young’s modulus. AlCu2Mn has the highest intrinsic hardness among AlCu2M compounds, according to calculations of their intrinsic hardness. The electronic densities of states are discussed in detail; it was discovered that all AlCu2M compounds form Al-Cu and Al-M covalent bonds. Additionally, we observe that the Debye temperature and minimum thermal conductivity of AlCu2Mn and AlCu2Sc are both larger than those of others, indicating stronger chemical bonds and higher thermal conductivities, which is consistent with the elastic modulus results.