Abstract: To efficiently and accurately analyze the electromagnetic properties of three-dimensional multilayer anisotropic Debye dispersive media, this paper proposes a fast-transfer matrix method (F-TMM). Starting from Maxwell's curl equations, the method derives the governing equations for anisotropic Debye dispersive media by utilizing the known transverse vectors of plane waves. Through simplification and computation of the governing equations, the eigenvalues of the anisotropic Debye dispersive media are systematically solved. By leveraging the tangential continuity conditions of electric and magnetic fields at interfaces, the transfer matrix within multilayer media is constructed, thereby obtaining the reflection and transmission coefficients in anisotropic Debye dispersive media. Two numerical experiments on uniaxial and biaxial anisotropic Debye dispersive media are designed, and a numerical comparison of propagation coefficients is conducted. The results demonstrate that compared with COMSOL software, CST software, and the traditional-transfer matrix method (T-TMM), F-TMM achieves a norm error of less than 10⁻³ in calculation results, while saving at least 46.6% in computational memory and 68.1% in CPU time, respectively. This method provides a reliable and efficient computational tool for investigating the electromagnetic characteristics of anisotropic Debye dispersive media.