In this paper, the surface enhanced Raman scattering (SERS) characteristics of Au and Au@Al2O3 nanoparticle dimers were calculated and analyzed by using finite element method (3D-FEM). Firstly, the electric field enhancement factors of Au nanoparticles at the dimer gap were optimized from three aspects: the incident angle of the incident light, the radius of nanoparticle and the distance of the dimer. Then, aluminum oxide is wrapped on the Au dimer. What is different from the previous simulation is that Al2O3 shell and Au core are regarded as a whole and the total radius of Au@Al2O3 dimer is controlled to remain unchanged. By comparing the distance of Au nucleus between Au and Au@Al2O3 dimer, it is found that the electric field enhancement factor of Au@Al2O3 dimer is much greater than that of Au dimer with the increase of Al2O3 thickness. The peak electric field of Au@Al2O3 dimer moves towards the middle of the resonance peak of the two materials, but the peak electric field of Au dimer is more concentrated than that of Au dimer, so that the excitation wavelength has less influence on Raman enhancement. The maximum electric field enhancement factor 583 is reached at the shell thickness of 1 nm. Our results provide a theoretical reference for the design of SERS substrate and the extension of the research scope.