In this study, we used the first-principles calculation method based on density functional theory to study sys-tematically the structural, mechanical, electronic, magnetic and thermodynamic properties of Fe2YAl (Y = Cr, Mo and W) full-Heusler alloys with Cu2MnAl configuration. The calculation results of mechanical properties showed that the Fe2YAl (Y = Cr, Mo and W) full-Heusler alloys have mechanical and thermodynamic stability, and they are all ductile materials, and all exhibit anisotropic behavior. The calculation results of electronic properties showed that these three alloys are all ferromagnetic metal materials and have thermodynamic stability. The calculated results of magnetic properties showed that they all have ferromagnetic metal behavior, and the total magnetic moment is not an integral multiple of the Bohr magneton. Finally, the quasi-harmonic Debye model is used to calculate and analyze the thermodynamic properties of the Fe2YAl (Y = Cr, Mo and W) full-Heusler alloys in the pressure range of 0-50 GPa and the temperature range of 0-800 K in detail. It is due to that they have been important guiding significance for future related research, and may become potential candidate materials for industrial applications.