In the field of image fusion, promising progress has been made by modeling data from different modalities as linear subspaces. However, in practice, the source images are often located in a non-Euclidean space, where the Euclidean methods usually cannot encapsulate the intrinsic topological structure. Typically, the inner product performed in the Euclidean space calculates the algebraic similarity rather than the semantic similarity, which results in undesired attention output and a decrease in fusion performance. While the balance of low-level details and high-level semantics should be considered in infrared and visible image fusion task. To address this issue, in this paper, we propose a novel attention mechanism based on Grassmann manifold for infrared and visible image fusion (GrFormer). Specifically, our method constructs a low-rank subspace mapping through projection constraints on the Grassmann manifold, compressing attention features into subspaces of varying rank levels. This forces the features to decouple into high-frequency details (local low-rank) and low-frequency semantics (global low-rank), thereby achieving multi-scale semantic fusion. Additionally, to effectively integrate the significant information, we develop a cross-modal fusion strategy (CMS) based on a covariance mask to maximise the complementary properties between different modalities and to suppress the features with high correlation, which are deemed redundant. The experimental results demonstrate that our network outperforms SOTA methods both qualitatively and quantitatively on multiple image fusion benchmarks. The codes are available at https://github.com/Shaoyun2023.