We proposed a model to investigate the transient diffusion of drug (sulphate) into the intervertebral disc. Using finite element method, drug diffusion was simulated and the concentration of diffused drug in each region of disc including Nucleus pulpous (NP), Inner annulus fibroses (IA), and Outer annulus fibroses (OA) was measured. In addition, to investigate the role of CEP permeability on the amount of diffused drug, model was simulated with different cartilage endplate (CEP) permeability. Having obtained concentration distribution for different cases, it was clearly shown that the amount of diffused drug is affected by the endplate permeability and the more permeable CEP, the more diffused drug into the disc specifically at the center of the disc.