Abstract Multi-modal fusion has been widely involved in focuses on the modern artificial intelligence research, e.g., from visual content to languages and backward. Common-used multi-modal fusion methods mainly include element-wise product, elementwise sum, or even simply concatenation between different types of features, which are somewhat straightforward but lack in-depth analysis. Recent studies have shown fully exploiting interactions among elements of multi-modal features will lead to a further performance gain. In this paper, we put forward a new approach of multi-modal fusion, namely Multi-modal Circulant Fusion (MCF). Particularly, after reshaping feature vectors into circulant matrices, we define two types of interaction operations between vectors and matrices. As each row of the circulant matrix shifts one elements, with newly-defined interaction operations, we almost explore all possible interactions between vectors of different modalities. Moreover, as only regular operations are involved and defined a priori, MCF avoids increasing parameters or computational costs for multi-modal fusion. We evaluate MCF with tasks of video captioning and temporal activity localization via language (TALL). Experiments on MSVD and MSRVTT show our method obtains the state-of-the-art performance for video captioning. For TALL, by plugging into MCF, we achieve a performance gain of roughly 4.2% on TACoS.