Recently, freedom in design of composite microstructure has been improved due to the development of the manufacturing technology of various shapes and diameters of carbon fibers. In other words, numerous candidates of composite microstructure should be considered toward a microscopic optimization of composite. To this end, two kinds of computational techniques were introduced in this study; homogenization method using key degree of freedom (DoF), and extended finite element method (XFEM). In order to evaluate an effect of microstructure on the macroscopic mechanical and fracture properties, homogenization method was introduced. Here, the key DoF method was utilized to simply handle the periodic boundary conditions. Additionally, the composite microstructure (fiber/ matrix interface) can be modeled independently of the mesh by the XFEM. This makes it possible to conduct comprehensive numerical investigation into various microstructures without remeshing.