Map construction task plays a vital role in providing precise and comprehensive static environmental information essential for autonomous driving systems. Primary sensors include cameras and LiDAR, with configurations varying between camera-only, LiDAR-only, or camera-LiDAR fusion, based on cost-performance considerations. While fusion-based methods typically perform best, existing approaches often neglect modality interaction and rely on simple fusion strategies, which suffer from the problems of misalignment and information loss. To address these issues, we propose MapFusion, a novel multi-modal Bird's-Eye View (BEV) feature fusion method for map construction. Specifically, to solve the semantic misalignment problem between camera and LiDAR BEV features, we introduce the Cross-modal Interaction Transform (CIT) module, enabling interaction between two BEV feature spaces and enhancing feature representation through a self-attention mechanism. Additionally, we propose an effective Dual Dynamic Fusion (DDF) module to adaptively select valuable information from different modalities, which can take full advantage of the inherent information between different modalities. Moreover, MapFusion is designed to be simple and plug-and-play, easily integrated into existing pipelines. We evaluate MapFusion on two map construction tasks, including High-definition (HD) map and BEV map segmentation, to show its versatility and effectiveness. Compared with the state-of-the-art methods, MapFusion achieves 3.6% and 6.2% absolute improvements on the HD map construction and BEV map segmentation tasks on the nuScenes dataset, respectively, demonstrating the superiority of our approach.