Abstract: The investigation of multiscale homogenization of metamaterial has important theoretical and application value.Among the existing theories of homogenization of metamaterial,the electromagnetic(EM)characteristics of vector fields are not fully considered.Considering the micro-scale characteristic of the periodic structure and the divergence and curl characteristics of EM field,a new vector correction is proposed to describe the micro-scale EM characteristics,which both the irrotational field and the non-divergence field are considered,so the new micro-scale functions are obtained.By using the multiscale functions and multiscale finite element method(FEM)based on the edge-based vector basis functions,the effective EM parameters and the E-field distributions of periodic composite materials are calculated. Compared with FEM,it is shown that the multiscale FEM can calculate the EM parameters and E-field effectively.