The electromagnetic scattering by an inhomogeneous conducting-gyroelectric object is investigated. A rigorous full-wave method based on the surface-volume integral equation (SVIE), in conjunction with Dini series expansion, is developed. A new orthogonal set of Dini-type spherical vector wave functions is constructed that allows the direct satisfaction of the boundary conditions on the conductor's surface, and in sequence, the reduction of the SVIE to an algebraic form. We investigate the validity of the developed method, which is next applied to radar cross section and interior field computations.