In this study, a two dimensional numerical advection diffusion model was developed to simulate an oil spill and to determine the fate and transport of oil on a sea surface. A meshless numerical scheme based on the Radial Basis Function Collocation method (RBFCM) was employed for solving the transport equation in the model. To evaluated the performance of the model, a benchmark problem and an application for the Marmara Sea were investigated. For the benchmark problem, several RBFCM solutions were investigated and compared to the analytical solutions. For the Marmara Sea application, only surface currents were used to drive the oil slick. Surface current profile was generated by interpolation of the data received from Office of Navigation, Hydrography and Oceanography using the Radial Basis Function Collocation method. Physical parameters of oil for diffusion, evaporation, vertical dispersion, shoreline deposition were based on literature values. Sensitivity analysis to key diffusion coefficients were conducted. Three events for each four months (January, April, July and October) were used to test the model.