This work provides mesoscale models for the anomalous diffusion of a polymer chain on a heterogeneous surface with rearranging randomly distributed adsorption sites. Both the “bead-spring” model and oxDNA model were simulated on supported lipid bilayer membranes with various molar fractions of charged lipids, using Brownian dynamics method. Our simulation results demonstrate that “bead-spring” chains exhibit sub-diffusion on charged lipid bilayers which agrees with previous experimental observations for short-time dynamics of DNA segments on membranes. In addition, the non-Gaussian diffusive behaviors of DNA segments have not been observed in our simulations. However, a simulated 17 base pairs double stranded DNA, using oxDNA model, performs normal diffusion on supported cationic lipid bilayers. Due to the number of positively charged lipids attracted by short DNA is small, the energy landscape that the short DNA experiences during diffusion is not as heterogeneous as that experienced by long DNA chains, which results in normal diffusion rather than sub-diffusion for short DNA.