An efficient finite element method-boundary element method (FEM-BEM) is proposed for electromagnetic analysis of inhomogeneous objects. The problem domain is discretized and evaluated with FEM, and the BEM introduces a truncated boundary on the surface of the domain utilizing boundary integral equations (BIEs) technique. To guarantee the precision, much dense discretization is usually required when modeling and simulating the inhomogeneous media, which will lead to a large and dense impedance matrix from the BEM part. Therefore, the nested complex source beam (NCSB) method is proposed in the FEM-BEM system to accelerate the evaluation of the BIEs, where the interaction between far-field groups is equivalent to that of the complex source beams located on the equivalent sphere of each group in an aggregation, translation and disaggregation process. Furthermore, the adaptive grouping technique for the NCSB is employed to improve the performance of the solution. Numerical results show the efficiency of the proposed method.