Fundus imaging plays a crucial role in diagnosing and monitoring various ocular diseases. The reliability of diagnostic outcomes heavily depends on the quality of the acquired images. Various factors may affect the image quality, such as environmental conditions and equipment malfunctions. However, the current methods of fundus quality assessment (FQA) mainly employ CNN-based architectures to extract local features, causing that the global features are ignored. To this end, we introduce Dual-Branch Cross Interaction Network for fundus quality assessment, called DCI-FQA, which consists of a parallel structure to capture both local and global features related to fundus quality. Specifically, the local and the global features extracted by CNN-branch and Swin-branch, respectively, which are mutually interacted in the spatial domain through attention modules. The quality-based features from dual-branch can be integrated by interacting features across different branches to improve the classification performance. Subsequently, the features of dual-branch and the fusion features are aggregated to classifier for the classification of quality assessment. The experiments on the FQ dataset demonstrate that the proposed method achieves the superior classification performance for fundus quality assessment.