We solve the problem of light scattering by a core-mantle spheroidal particle in the case when the external and internal boundaries of the mantle are concentric, coaxial, but not confocal. We expand the fields in terms of spheroidal wave functions related to the different boundaries and operate with the expansions using the surface integral formulation of the problem. By applying some relations between spherical and different spheroidal functions, we derive the so-called T-matrix connecting the expansion coefficients for the incident and scattered fields. We transform such a “spheroidal” T-matrix to the standard one that arises for the spherical basis widely used in applications. Numerical calculations demonstrate that this approach is as efficient as that for homogeneous spheroids. Moreover, we find that it appears to be the only way to accurately derive the T-matrix for layered spheroidal particles in a broad range of parameter values.