Thermoelectric (TE) materials are an important class of energy materials that can directly convert thermal energy into electrical energy. Screening high-performance thermoelectric materials and improving their TE properties are important goals of TE materials research. Based on the objective relationship among the molar Gibbs free energy (Gm), the chemical potential, the Fermi level, the electronegativity (X) and the TE property of a material, a new method for screening TE materials with high throughput is proposed. This method requires no experiments and no first principle or Ab initio calculation. It only needs to find or calculate the molar Gibbs free energy and electronegativity of the material. Here, by calculating a variety of typical and atypical TE materials, it is found that the molar Gibbs free energy of Bi2Te3 and Sb2Te3 from 298 to 600 K (Gm = -130.20~-248.82 kJ/mol) and the electronegativity of Bi2Te3 and Sb2Te3 and PbTe (X = 1.80~2.21) can be used as criteria to judge the potential of materials to become high-performance TE materials. For good TE compounds, Gm and X are required to meet the corresponding standards at the same time. By taking Gm = -130.20~-248.82 kJ/mol and X = 1.80~2.21 as screening criteria for high performance TE materials, it is found that the Gm and X of all 15 typical TE materials and 9 widely studied TE materials meet the requirement very well, except for the X of Mg2Si, and 64 pure substances are screened as potential TE materials from 102 atypical TE materials. In addition, with reference to their electronegativity, 44 pure substances are selected directly from a thermochemical data book as potential high-performance TE materials. A particular finding is that several carbides, such as Be2C, CaC2, BaC2, SmC2, TaC and NbC, may have certain TE properties. Because the Gm and X of pure substances can be easily found in thermochemical data books and calculated using the X of pure elements, respectively, the Gm and X of materials can be used as good high-throughput screening criteria for predicting TE properties.