The first-principle approach for calculating the D. C. conductivities of the composites is discussed systematically. The integral equation for determining the effective conductivities of the composites with local anisotropic componentes is derived, and a convenient method for calculating effective conductivity tensor is proposed. We have dealt with effective conductivity tensor of the composites with local anisotropic components. A theoretical method which can treat the more common composites with no periodicity is developed. A new approximate method for solving integral equation by means of expansion with two bases is also proposed, by which we can calculate composites with large porosity and complicate structure with high precision, and it could have the advantage of saving lot of computing time.