Abstract A statistical-thermodynamic model for binary nonstoichiometric A 5 B 3 with D8 1 -structure has been established on the basis of the grand canonical ensemble. In the model the average chemical potentials according to the composition and a new extra equation as a boundary condition are proposed for more accuracy and free experimental data calculations. The model can be used in any A 5 B 3 type compounds with D8 1 structure. The establishment method of the statistical-thermodynamic model can be extended to other complicated structures. We apply the statistical-thermodynamic model to α-Nb 5 Si 3 and the parameters used in the model are obtained from the first-principles' calculations. From these parameters the expression for the point defect concentrations as a function of compositions and temperatures is obtained by numeral calculations. The constitutional defects and thermal defects in α-Nb 5 Si 3 are discussed.