A fast solution to the electromagnetic scattering by large-scale three-dimensional magnetodielectric objects with arbitrary permittivity and permeability is presented. The scattering problem is characterized by using coupled field volume integral equation (CF-VIE). By considering the total electric and magnetic fields, i.e., the sum of incident fields and the radiated fields by equivalent electric and magnetic volume currents, the CF-VIE can be established in the volume of the scatterers. The resultant CF-VIE is discretized and solved by using the method of moments (MoM). For large-scale scattering problems, the adaptive integral method (AIM) is then applied in the MoM in order to reduce the memory requirement and accelerate the matrix-vector multiplication in the iterative solver. The conventional AIM has been modified to cope with the two sets of equivalent volume currents.