In this article, we consider an anomalous diffusion model in a planar polymeric matrix as a space fractional diffusion problem with moving boundary conditions. An iterative implicit finite difference method with variable time‐steps is established to solve the proposed problem. The stability and consistency of the numerical method are proved and the estimation of the numerical error is conducted. The numerical results are compared with the scale‐invariant and homotopy perturbation solutions when the diffusion coefficient is a constant. Furthermore, the numerical results for a test case with time‐dependent diffusion coefficient are reported.