Nowadays oil spill are one of the most important problem in the humans life. Usually advection and dispersion occur because of chemicals, physicals and biological processes that related by properties of oil and other things. These processes are evaporation, dispersion and so on. When oil spills on the sea, it is extended and made oil slick. Increasing these kinds of events cause developing many kind of oil spill model. In this paper a numerical model for simulating drifting and spreading of oil slick thickness including dissipative processes such as advection and diffusion of averaged oil concentration in the water column and evaporation, with Eulerian approach and multi phase model has been developed. Equations were discrete using finite volume method. Available hydrodynamic model can solve two-dimensional depth-averaged unsteady Navier-Stokes equations. Alternating Direction Implicit method (ADI) is used for numerical solution of flow. In order to verify the accuracy of hydrodynamic, advection and diffusion model of oil slick thickness and oil average concentration, numerical results compared with experimental measurements and analytical model. Comparison shows the model can satisfactory simulate the problem.