Abstract- Optical and magneto-optical (MO) responses in magnetic multi-layer systems are calculated by transfer matrix method (TMM). In a bi-gyrotropic medium, electric permittivity (&epsilon) and magnetic permeability (&mu) coefficients are in the form of non-diagonal tensors, synchronously, which their non-diagonal elements refer to the existence of anisotropy in such medium. In this paper, a transfer matrix method-based approach, which is consisting of two boundary and propagation 4×4 matrices, has been provided for a bigyrotropic medium.