Based on the stretched coordinate perfectly matched layer (SC-PML) formulation and the auxiliary differential equation method, an absorbing boundary condition for general dispersive medium is presented, and applied to both the standard finite difference time domain (FDTD) method and the high-order FDTD method. The proposed D-H formulations are completely independent of the material properties of the FDTD computational domain. Thus they can be directly applied to the simulations involving arbitrary dielectrics. Numerical results show that compared with the CPML, the proposed method is versatile, has an improved absorbing performance and low computational complexity, and can substantially reduce the computational time.