This proposal is to observe single-spin diffusive motion on a two-dimensional (2D) percolating network having a fractal geometry. The random walker¿s travel times on a percolating network increase more rapidly with distance than they do on a homogeneous lattice due to the restricted number of paths connecting two points on a percolating network. As the result, the energy spectrum corresponding to the self correlation function exhibits a non-Lorentzian form of S(E) ~ E^-x with the exponent, x, related to the fractal structure. We try a clear detection of the anomalous spin diffusion in the non-Lorentzian energy spectrum of the self correlation function in the 2D Heisenberg percolating antiferromagnet, Rb2Mn0.6Mg0.4F4.