A discrete computer method, which considers the principal characteristics of the motion of discrete particles caused by the airflow over the aeolian bedforms using a set of simple rules, is suggested to simulate the initiation and evolution of wind blown sand ripples and dunes. The results indicate that, if the grain-bed impacting and surface creep are taken into account, the model is capable of reproducing sand ripples vividly, and describing the reparation of any destroy to rippled surface, a phenomenon observed in field. If the saltation driven by the main flow and the secondary flow, the surface creep due to gravity, and the slide occurring when the slope of sand surface is larger than the angle of repose are considered, the model can simulate the formation and development of sand dunes whose shape and arrangement in space are in accordance with the landscape of typical deserts. After a further investigation into the simulation process, we draw the conclusion that the aeolian bedformsis a system of self-organization and hierarchy with a fractal character.