Multisensor collaboration is a key technology in autonomous driving and environmental perception. Owing to the inevitable external force, the sensor shifts during the measurement process, thus necessitating a real-time dynamic calibration network. Therefore, this paper proposes a novel dynamic calibration network for Lidar and camera based on cost-volume construction (DC-LCNet). First, a dual-channel map comprising a depth map and reflection map is established as the network input, and the sparse point-cloud problem is solved using the features of radar point-cloud data. Additionally, to obtain high-quality discriminative features between the two modal data features, feature transformer is designed for both point-cloud and image modalities. Finally, a cost-volume construction quantity for stereo matching is proposed to describe the feature correlation between two modalities. The experimental results of the network on the KITTI dataset show translation and rotation errors of 0.246 cm and 0.021°, respectively, whereas those on the nuScences dataset indicate 0.336 cm and 0.053°, respectively. In terms of error calibration, the proposed network can manage variations of up to ±1.5 cm and ±20° for the translation and rotation errors, respectively. The most accurate network reported thus far exhibits translation and rotation errors of 0.380 cm and 0.048° on the KITTI dataset, respectively. The experimental results show that DC-LCNet enable new breakthroughs to the dynamic calibration of Lidar and cameras.