We report the preparation of novel quasi-one-dimensional (quasi-1D) C60 nanostructures on rippled graphene. Through careful control of the subtle balance between the linear periodic potential of rippled graphene and the C60 surface mobility, we demonstrate that C60 molecules can be arranged into a quasi-1D C60 chain structure with widths of two to three molecules. At a higher annealing temperature, the quasi-1D chain structure transitions to a more compact hexagonal close packed quasi-1D stripe structure. This first experimental realization of quasi-1D C60 structures on graphene may pave a way for fabricating new C60/graphene hybrid structures for future applications in electronics, spintronics and quantum information.