A novel auxiliary difference equation (ADE) finite-difference time-domain (FDTD) method with Crank-Nicolson (CN) scheme is proposed for electromagnetic simulation of dispersive materials in this letter. The proposed method introduces an ADE technique that establishes the relationship between the electric displacement vector and electric field intensity in dispersive media with a difference equation. Hence, the CN scheme is only applied to one of the Maxwell curl equations, resulting in reduced memory usage and computing time. To validate the advantages of the proposed approach, an example with plane wave propagation in a dispersive media is presented. Compared with the conventional ADE-CN-FDTD method, the proposed method consumes much less computing time while preserves excellent simulation accuracy.