The growth of graphene on 3C-SiC/Si heterostructure is a promising approach, which provides low production cost, high scalability and easiness of nanoelectromechanical system fabrication. However, the quality of graphene is still insufficient for device applications due to mediocre morphological and structural quality of the 3C-SiC epilayers compared to bulk SiC crystals and to excessive Si out-diffusion from the Si substrate. Here, we propose a solution of inserting a 4H-AlN layer between 3C-SiC and Si, which allows us to polish the 3C-SiC film without worrying about enhancement of the Si out-diffusion despite the thinning after the polishing. With this insertion, a considerable quality improvement is achieved in our graphene on silicon.