A three-dimensional finite element method for polycrystalline plasticity problems based on the homogenization method has been developed. The homogenization method is one of the useful procedures to combine behaviors in a macro-scale and a micro-scale with periodical structure satisfying physical and mathematical compatibility between those scales. Polycrystalline metals are assumed to have periodical microstructure, therefore, a three-dimensional polycrystalline model is introduced into the homogenization method. In the present method, each material point in the element is considered to be a polycrystalline aggregate of a number of FCC grains where the Taylor theory of crystal plasticity is assumed. It is shown that the proposed method can evaluate macroscopic material properties only with microscopic material information.