Extrinsic calibration on a LiDAR-camera system is an essential task for the advanced perception application for the intelligent vehicle. In the offline situation, a calibration object based method can estimate the extrinsic parameters in high precision. However, during the long time application of LiDAR-camera system in the actual scenario, the relative pose of LiDAR and camera has small and accumulated drift, so that the offline calibration result is not accurate. To correct the extrinsic parameter conveniently, we present a deep learning based online extrinsic calibration method in this paper. From Lambertian reflection model, it is found that an object with higher LiDAR intensity has the higher possibility to have salient RGB features. Based on this fact, we present a LiDAR intensity attention based backbone network (LIA-Net) to extract the significant co-observed calibration features from LiDAR data and RGB image. In the later stage of training, the loss of extrinsic parameters changes slowly, causing the risk of vanishing gradient and limiting the training efficiency. To deal with this issue, we present the structural consistency (SC) loss to minimize the difference between projected LiDAR image (i.e., LiDAR depth image, LiDAR intensity image) and its ground truth (GT) LiDAR image. It aims to accurately align the LiDAR point and RGB pixel. With LIA-Net and SC loss, we present the convolution neural network (CNN) based calibration network LIA-SC-Net. Comparison experiments on a KITTI dataset demonstrate that LIA-SC-Net has achieved more accurate calibration results than state-of-the-art learning based methods. The proposed method has both accurate and real-time performance. Ablation studies also show the effectiveness of proposed modules.