The adsorption and the growth of ZnO on alpha-Al2O3(0001) surface at various temperatures were theoretically calculated by using a plane wave pseudopotentials (USP) method based on density functional theory. The average adsorption energy of ZnO at 400, 600 and 800 degrees C is 4.16 +/- 0.08, 4.25 +/- 0.11 and 4.0.5 +/- 0.23 ev respectively. Temperature has a remarkable effect on the structure of the surface and the interface of ZnO/alpha-Al2O3(0001). It is found that the Zn-hexagonal symmetry deflexion does not appear during the adsorption growth of ZnO at 400 degrees C, and that the ZnO[10 (1) over bar0] is parallel with the [10 (1) over bar0] of the alpha-Al2O3(0001), which is favorable for forming ZnO film with the Zn-terminated surface. It is observed from simulation that there are two kinds of surface structures in the adsorption of ZnO at 600 degrees C: one is the ZnO surface that has the Zn-terminated structure, and whose [10 (1) over bar0] parallels the [10 (1) over bar0] of the substrate surface, and the other is the ZnO[10 (1) over bar0] // sapphire [11 (2) over bar0] with the O-terminated surface. The energy barrier of the phase transition between these two different surface structures is about 1.6 eV, and the latter is more stable. Therefore. the suitable temperature for the thin film growth of ZnO on sapphire is about 600 degrees C, and it facilitates the formation of wurtzite structure containing Zu-O-Zn-O-Zn-O double-layers as a growth unit-cell. At 600 degrees C. the average bond length of Zn-O is 0.190 +/- 0.01 nm, and the ELF value indicates that the bond of (substrate)-O-Zn-O has a distinct covalent character, whereas the (Zn)O-Al (substrate) shows a clear character of ionic bond. However, at a temperature of 800 degrees C, the dissociation of Al and O atoms on the surface of the alpha-Al2O3(0001) leads to a disordered surface and interface structure. Thus, the Zn-hexagonal symmetry structure of the ZnO film is not observed under this condition.