We have grown aluminum nitride (AIN) films on Si(110) substrates by pulsed laser deposition (PLD), and investigated the effects of laser power on the crystallinity and surface morphology of the AIN films. First, we epitaxially grew a fairly flat, high-quality AIN film, which contained no rotation domains, onto the Si(110) substrate in a well-lattice-matched relationship. Secondly, we formed a SiC interfacial buffer layer on the AIN film to grow a high-quality 3C-SiC film on the SiC buffer layer by PLD, which gave rise to a 3C-SiC(111)3x3 surface. The root-mean-square-roughness value of the SiC film was smaller than the previously reported values of SiC/AIN multilayers on Si(100) and Si(111) substrates. Thirdly, we grew graphene by annealing the SiC film at a high temperature in an ultra-high vacuum. It was demonstrated that the qualified graphene layer without rotation domains was grown on the SiC film. The formation of voids and the outdiffusion of Al and N atoms from the AIN film were successfully suppressed during the high-temperature annealing.