It has been observed in many cases that the effective dielectric constant of some general composite media can reach as high as thousands at low frequency side. In this paper, a numerical method is used to simulate this phenomenon and study the parameters which could affect the dielectric spectrum. In order to obtain the effective dielectric constant and conductivity of the composite and understand the dominant factors of large dielectric enhancement of low frequency side, a three-dimensional finite difference method (3D-FDM) is used to simulate general mixtures and mixtures with membrane structure. A special FDM grid is introduced to handle the membrane that coats the inclusions of the composite medium. We analyze the influence of the membrane thickness, membrane conductivity, inclusion insertion ratio, and inclusion shape on the effective dielectric constant and conductivity of the composite. The results show that: (1) the low-conductivity membrane may be the cause of the dielectric enhancement of low frequency side; (2) the membrane thickness, membrane conductivity, and inclusion insertion ratio can affect the dielectric enhancement level significantly; and (3) the physics of the dielectric enhancement is probably related to the frequency dependence of the effective plate separation of the capacitor model.