The present paper offers a numerical model which can be applied for the simulation of wave height distribution on a 2-D horizontal soft mud layer. The model is based on mild slope equations and it includes combined wave refraction, diffraction, reflection and breaking. The high energy dissipation of wave height due to the presence of fluid mud layer has also been simulated. Wave height attenuation is calculated from a multi-layered wave-mud interaction model considering the vertical distribution of water content ratio in fluid mud layer. The constitutive equations of visco-elastic-plastic model are assumed for the rheological behavior of fluid mud. An artificial neural network is used as a part of wave attenuation calculation to speed up the computation. Applying the model in the East Bay, Louisiana at the mouth of Mississippi River shows a reasonable agreement with the wave height measurements.