At present, high quality graphene is synthesized mainly by chemical vapor deposition. It is crucial to decompose and adsorb methane (CH4) on the surface of substrate before CH4 grows into graphene. The graphene is grown mainly on metal substrate due to the catalytic effect of metal. It is difficult to grow graphene thin film on the surface of non-metallic substrate, especially on the surface of -Al2O3 (0001). In this paper, the density functional theory based generalized gradient approximation method is applied to simulating the nucleation of graphene on -Al2O3 (0001) surface, synthesized by chemical vapor deposition. First, we establish a scientific -Al2O3 (0001) surface model, then simulate the decomposition process of CH4 on -Al2O3 (0001) surface by calculating the adsorption sites and adsorption configurations of groups and atoms. Finally, we investigate the groups of CH4 decomposition and atom coupling process on -Al2O3 (0001) surface. The results show that the CH3 groups, C and H atoms are preferentially adsorbed at the top of the O atoms, and the adsorption energies are -2.428 eV,-4.903 eV, and -4.083 eV, respectively. The CH2 and CH groups are preferentially adsorbed on the bridge between O and Al atoms with the adsorption energies of -4.460 eV and -3.940 eV, respectively. The decomposition of CH4 on -Al2O3 (0001) surface is an endothermic process. It requires higher energy and cross reactive energy barrier for CH4 to be completely decomposed into C atom, which makes it difficult that the C atom stays on the substrate surface. The coupling process among CH groups on the surface of -Al2O3 (0001) is an exothermic process. When CH and CH groups are coupled, the energy of the system decreases by 4.283 eV. When (CH)2 and CH groups are coupled, the energy of the system decreases by 3.740 eV. The (CH)x can be obtained by continuous migration and coupling between the CH groups on the surface of the -Al2O3 (0001), and (CH)x group is a precursor of graphene growth. The energy of the system decreases in the process. The above results show that the activated atom or group of graphene nucleation is not C atom but CH group. The CH group migration and aggregation on the surface of -Al2O3 (0001) give priority to the formation of lower energy (CH)x structure. In order to better understand the microscopic growth process of graphene on sapphire, it is important to study the role of (CH)x in the surface of sapphire for revealing the nucleation mechanism of graphene.