The most popular coastal diffusion modelling technique is the traditional particle tracking method which can only model Fickian diffusion. However, in reality, non-Fickian diffusion dispersion in coastal surface waters has been observed by some researchers. A new Particle Tracking technique is introduced in this article that generates non-Fickian diffusion by employing fractional Brownian motion (fBm). The authors found that for coastal surface waters, the Hurst exponent H is not restricted to the range 0 ~ 1. A newly developed Particle Tracking method that generates non-Fickian diffusion by employing accelerated fractional Brownian motion (AfBm) has been first studied and introduced. Numerical techniques to model the non-Fickian spreading observed in the real coastal data have been successfully developed and the simulation results are encouraging when compared with the observed data and the results of conventional dispersion modelling.