Subsurface scattering is a key factor in ensuring the visual effects of translucent materials, and it holds significant application value in film, gaming, virtual reality, and digital twin technology. However, existing technologies rely on planar diffusion profiles, which lead to issues such as color distortion and harsh shadow transitions when rendering complex surfaces. To address these issues, this paper proposes a pre-integration method based on multipole theory to enhance the accuracy of subsurface scattering on surface models. Initially, it employs the multipole model to build accurate single-layer and multi-layer diffusion profiles for surfaces. Subsequently, these diffusion profiles are pre-integrated into a Lookup Table (LUT), and single scattering is included to further improve the scattering precision. Lastly, during real-time rendering, texture blur techniques are used in conjunction with LUT to improve the accuracy of the average curvature. Moreover, the paper discusses the contribution of transmitted light to the scattering effect in order to enhance the scattering in specific scenarios. Experiments focused on facial rendering demonstrate that the proposed method outperforms existing pre-integration techniques in error metrics such as SSIM and RMSE, and effectively eliminates previous errors in surface scattering while maintaining rendering speed and significantly enhancing the realism of the render.