Abstract: This paper applies a random walk method to simulate scalar transport and dispersion in vertical two-dimensional wave flows. First, this Lagrangian model is verified against an idealized problem involving unsteady shear flows, and a good agreement between the simulated and analytical values of dispersion coefficient and demonstrates its validity. Then, flow velocities and water surface profiles of the water waves are formulated based on the linear and second order Stokes wave theories. The wave flows and their longitudinal dispersion coefficients are numerically simulated and compared between the two theories, showing high accuracy of the random walk method. We also discuss the choice of the control parameters in the model, such as particle number and time step, for a good balance between the computational cost and accuracy. Finally, parameter sensitivity is analysed. We find that longitudinal dispersion coefficient is, as expected, inversely proportional to diffusion coefficient or wave period, while it increases with the increase in water depth and wave height.