LiDAR and cameras are two complementary sensors for 3D perception in autonomous driving. LiDAR point clouds have accurate spatial and geometry information, while RGB images provide textural and color data for context reasoning. To exploit LiDAR and cameras jointly, existing fusion methods tend to align each 3D point to only one projected image pixel based on calibration, namely one-to-one mapping. However, the performance of these approaches highly relies on the calibration quality, which is sensitive to the temporal and spatial synchronization of sensors. Therefore, we propose a Dynamic Cross Attention (DCA) module with a novel one-to-many cross-modality mapping that learns multiple offsets from the initial projection towards the neighborhood and thus develops tolerance to calibration error. Moreover, a \textit{dynamic query enhancement} is proposed to perceive the model-independent calibration, which further strengthens DCA's tolerance to the initial misalignment. The whole fusion architecture named Dynamic Cross Attention Network (DCAN) exploits multi-level image features and adapts to multiple representations of point clouds, which allows DCA to serve as a plug-in fusion module. Extensive experiments on nuScenes and KITTI prove DCA's effectiveness. The proposed DCAN outperforms state-of-the-art methods on the nuScenes detection challenge.