As an essential procedure of data fusion, LiDAR-camera calibration is critical for autonomous vehicles and robot navigation. Most calibration methods require laborious manual work, complicated environmental settings, and specific calibration targets. The targetless methods are based on some complex optimization workflow, which is time-consuming and requires prior information. Convolutional neural networks (CNNs) can regress the six degrees of freedom (6-DOF) extrinsic parameters from raw LiDAR and image data. However, these CNN-based methods just learn the representations of the projected LiDAR and image and ignore the correspondences at different locations. The performances of these CNN-based methods are unsatisfactory and worse than those of non-CNN methods. In this paper, we propose a novel CNN-based LiDAR-camera extrinsic calibration algorithm named CFNet. We first decided that a correlation layer should be used to provide matching capabilities explicitly. Then, we innovatively defined calibration flow to illustrate the deviation of the initial projection from the ground truth. Instead of directly predicting the extrinsic parameters, we utilize CFNet to predict the calibration flow. The efficient Perspective-n-Point (EPnP) algorithm within the RANdom SAmple Consensus (RANSAC) scheme is applied to estimate the extrinsic parameters with 2D–3D correspondences constructed by the calibration flow. Due to its consideration of the geometric information, our proposed method performed better than the state-of-the-art CNN-based methods on the KITTI datasets. Furthermore, we also tested the flexibility of our approach on the KITTI360 datasets.