Multimodal MR image synthesis aims to generate missing modality image by fusing and mapping a few available MRI data. Most existing approaches typically adopt an image-to-image translation scheme. However, these methods often suffer from sub-optimal performance due to the spatial misalignment between different modalities while they are typically treated as input channels. Therefore, in this paper, we propose an Adaptive Group-wise Interaction Network (AGI-Net) that explores both inter-modality and intra-modality relationships for multimodal MR image synthesis. Specifically, groups are first pre-defined along the channel dimension and then we perform an adaptive rolling for the standard convolutional kernel to capture inter-modality spatial correspondences. At the same time, a cross-group attention module is introduced to fuse information across different channel groups, leading to better feature representation. We evaluated the effectiveness of our model on the publicly available IXI and BraTS2023 datasets, where the AGI-Net achieved state-of-the-art performance for multimodal MR image synthesis. Code will be released.