Anisotropic dielectrics and ferromagnetic materials are widely used in dispersion-engineered metamaterials. For example, nonreciprocal magnetic photonic crystals (MPhCs) are periodic structures whose unit cell is composed of two misaligned anisotropic dielectric layers and one ferromagnetic layer and they have extraordinary characteristics such as wave slowdown and field amplitude increase. We develop an unconditionally stable complex-envelop alternating-direction-implicit finite-difference time-domain method (CE-ADI-FDTD) suitable for the transient analysis of anisotropic dielectrics and ferromagnetic materials. In the proposed algorithm, the perfectly-matched-layer (PML) is straightforwardly incorporated in Maxwell's curl equations. Numerical examples show that the proposed PML-CE-ADI-FDTD method can reduce the CPU time significantly for the transient analysis of anisotropic dielectrics and ferromagnetic materials while maintaining computational accuracy.