A higher figure-of-merit Z of a thermoelectric material shows a higher performance at a specific narrow temperature range. On the other hand, the specific temperature can be shifted to higher temperature by increasing the carrier concentration. Bismuth telluride(Bi2Te3), lead telluride(PbTe) and Si-Ge alloy(SiGe) are used for low, medium and high temperature range, respectively. Usually, a monolithic and uniform thermoelectric material is used, though a temperature gradient exists in the thermoelectric material. Therefore, each part has not proper carrier concentration for each temperature. Two times of higher performance than a traditional thermoelectric material can be expected, if the proper carrier concentration gradient is performed to fit with the temperature gradient. Performing stepwise change of carrier concentration is also a performing method for practical application. That is a fundamental concept of energy converting FGM. A national project by STA was started to develop the FGM in 1993. It is essential to choose a proper material for each part to fit the temperature gradient. The proper material is a material with proper carrier concentration and a proper compound to match the temperature of each part along the temperature gradient. FGM joining of these materials and fitting electrodes with FGM interface are also core technique, because thermal stress relaxation caused by the difference of thermal expansion coefficient is important at a high temperature. Joining two Bi2Te3 with carrier concentrations n(e) of 1.0 and 4.5 x 10(25) was prepared by ordinal soldering technique or diffusion bonding. The specific temperature range of Seebeck coefficient alpha for the joined Bi2Te3 is extended from 50 to 100K, and the value of alpha at the valley between two materials with different n(e) was higher than both materials. The sintered n-type PbTe FGM with 3 layers of n(e) = 3.51, 2.60 and 2.26 x 10(25) was prepared by hot pressing. The effective maximum power P-max of the FGM at the temperature difference of Delta T=310K is 150Wm/m(2) and is about 7% lager than that of the layer with n(e) =3.51x10(25) whose P-max is the greatest in all layers.