Brain image registration is essential for analyzing both group-level commonalities and individual deviations. Traditionally, brain image registration has been primarily performed within the same species. However, this study aims to propose a method for the registration of the standard brains of different species, particularly those of common marmosets and humans. Successful registration between these brains is expected to facilitate discussions on how human-specific functions were acquired through evolution, based on structural differences. To achieve this goal, we employed a brain image registration method based on Implicit Neural Representations. Furthermore, we set an objective function that integrates multiple imaging modalities, including structural MRI images suitable for examining differences in cortical structures, diffusion MRI images, and mask images representing correspondences of functional areas. As a result, we found that our new approach enabled significantly better 3D registration between the two species compared to conventional image registration methods such as Advanced Normalization Tools (ANTs), which have been widely used in the past.