Predicting fluid cognition via neuroimaging data is essential for understanding the neural mechanisms underlying various complex cognitions in the human brain. Both brain functional connectivity (FC) and structural connectivity (SC) provide distinct neural mechanisms for fluid cognition. In addition, interactions between SC and FC within distributed association regions are related to improvements in fluid cognition. However, existing learning-based methods that leverage both modality-specific embeddings and high-order interactions between the two modalities for prediction are scarce. To tackle these challenges, this study proposes an end-to-end brain structure-function interaction network that incorporates both modality-specific embeddings and structure-function interactions to predict fluid cognition. In this model, we generate embeddings from both FC and SC separately using a graph convolution encoder-decoder module. Subsequently, we learn the interactive weights between corresponding regions of FC and SC, reflecting the coupling strength, by employing an interactive module on the embeddings of both modalities. A novel graph structure - utilizing modality-specific embeddings and interactive weights - is constructed and used for the final prediction. Experimental results demonstrate that our proposed method outperforms other state-of-the-art methods employed on uni-modal and multi-modal brain features. We further identify that strong structure-function coupling in the inferior frontal, postcentral, superior temporal and cingulate cortices are associated with fluid intelligence.