A numerical model is newly developed to describe the behavior of a pollutant in a coastal environment. In the model, the advection-diffusion-reaction equation is solved by employing a split operator technique. The advection part is first solved by SOWMAC and the diffusion part is then solved by a three-level locally implicit scheme. The newly developed model is verified by applying to idealized problems. The model yields excellently agreeable results to analytical solutions. The model is then applied to a spreading of pollutant material in a coastal zone.