Based on the rst-principles calculation and Mahan-Sofo s theory, we calculated the electronic structure and the thermoelectric gure of merit of Ce 3 Te 4 under different pressures. The peak of DOS for Ce 3 Te 4 shows the form of Dirac delta function around Fermi level. When the pressure is 1.1 GPa, the height of DOS peak is higher than those under other pressures, and the full width at half maximum is the narrowest. The thermoelectric gure of merit of Ce 3 Te 4 under 1.1 GPa, 1.3 GPa, and 2.5 GPa pressure is the highest, which is just below 14.0. This illustrates that the appropriate pressure could change the electronic structure of Ce 3 Te 4 , and improves the thermoelectric properties of Ce 3 Te 4 .