In the implementation of autonomous driving, high-precision maps and environment perception are required to support the driving process. They are commonly used to fuse image and point cloud data, but it is necessary to obtain the external parameters of the camera and radar when performing data fusion. However, the external parameters of the camera and radar can cause problems that can be solved by joint calibration. For fast, accurate acquisition of external parameters, a special three-plane calibration plate is designed to fit the spatial equations for each of three different planes passing through the initial point clouds in this study. The calibration plate is used to obtain the coordinates of feature points in the radar coordinate system through the spatial relationships and to extract the pixel coordinates of the feature points from the images to establish the corresponding equations. Finally, the least squares method is used to obtain the calibration parameters. The experimental results show that this method can obtain calibration results faster and more robustly than the traditional checkerboard grid calibration method.