The structural, elastic, electronic, and thermal properties of Ti-Al-Me (Me=Cu, Fe and Ni) alloys (TAMs) with the face-centered cubic phase were investigated using plane-wave pseudo potential method which is implemented in CASTEP code in the framework of density functional theory. The stability of the structure was confirmed from energetic, mechanical and phonon dynamic perspectives. Based on the calculated elastic constants combined with empirical and semi-empirical formulas, physical properties including ductility/brittleness, hardness and anisotropy of each phase was calculated. Moreover, thermodynamic information such as entropy, enthalpy, free energy, heat capacity and heat transfer coefficient were calculated. The results showed that TiAlFe2 had the highest thermal conductivity coefficient, and the heat capacities of all phases gradually approached the Dulong-Petit limit at high temperatures, while they conformed to the Debye T3 temperature law at low temperatures. Furthermore, the electronic structure calculation results indicate that all compounds are metallic and the d orbital of each atom plays an important role in the hybridization process. These calculation results are of great practical importance for understanding the basic physical and chemical properties of TAMs, clarifying their application and making sensible material selection.