In this paper the mode decomposition approach in the studies of the synchronization of the coupled dynamical systems is generalized to the case of the coupled non-identical dynamical systems by changing the coupling function. The synchronization of the non-identical periodic and quasi-periodic attractor systems is considered detailedly and the conditions for their local synchronization stability are obtained in this paper. The numerical simulation is performed and it was found that the dynamical behaviors of the synchronization are rich. The behaviors include stable synchronized periodic and quasi-periodic solutions in the coupled non-identical quasi-periodic attractor systems，and several stable synchronized periodic solutions in the coupled non-identical periodic attractors， where the new stable synchronized periodic solutions are born due to the coupling，and their attraction basins differe greatly，i.e.，in both of them the multiplicity of the synchronization appears. At the same time the validity of the mode decomposition is also verified.