An effective hybrid method is proposed, which combines the method of moments (MoM), the finite element method (FEM) and the wavelet transform method (WTM) (referred to as MoM/FEM/WTM method) for efficient solutions of scattering problems involving inhomogeneous media. The hybrid technique applies the equivalence principle to transform the original problem into interior and exterior problems which are coupled on the shared boundary through the continuity conditions of the tangential electric and magnetic fields. The MoM and the WTM are used for efficient solutions of the exterior problem and the FEM for the interior problem. In contrast to other traditional hybrid techniques, the new hybrid method, which combines the advantages of the MoM, the FEM and the WTM, can always produce highly sparse moment matrix equations which can be solved efficiently. This is of particular importance for large-size electromagnetic problems. Numerical results are given to demonstrate the merit of the method.