The Finite Element Method (FEM) can be well applied to find the solution of inhomogeneous, closed boundary problems when the size is small. On the contrary, the Boundary Element Method(BEM) is more powerful than the FEM especially for homogeneous open boundary problems. In this paper, it is shown that the FEM-BEM Hybrid method can be well applied in the field of inhomogeneous, open boundary dielectric scattering problems. To check the accuracy of this method we calculated electromagnetic scattering from 3-layer dielectric circular cylinder, and compared with the analytic solution.