By using the classical molecular dynamics and the simulated annealing techniques, the evolutions of the rippled morphology in single atomic graphenes placed on the Si (100), Si (111) and Si (211) surfaces respectively are performed at an atomic level. Our results show that the monolayer graphene sheets on the different Si surfaces form atomic scale rippled structures. A graphene monolayer prepared on Si surface forms rippled structure due to the relative lattice mismatch between graphene and Si substrate. The rippled morphology of graphene sheet on Si surface is strongly dependent on the annealing temperature. Such ripples will directly affect the adhesion strength between graphene and Si substrate. These findings are useful for understanding the structural morphology and stability of graphene on the semiconductor Si substrate, which will provide an analysis reference for further applications of graphene.