Simultaneous Localization and Mapping (SLAM) is a significant research topic in robotics since it is one of the key technologies for robot automation. Although lidar-based SLAM methods have achieved promising performance, traditional lidar SLAM methods still produce large vertical errors. To address this issue, we propose a feature extraction and vertical optimized lidar odometry and mapping approach. Firstly, we optimize the feature extraction. Specifically, we propose a more accurate ground segmentation approach and a new curvature definition, which is used to extract more discriminative features. Additionally, we propose a lidar mapping approach, which adds new vertical residuals and pitch residuals to the objective function. Then a two-step Levenberg-Marquardt method is used to solve the pose transformation. Finally, we evaluate the proposed method in public datasets and real environments. Experiments show that compared with other state-of-the-art methods, our method achieves better accuracy and reduces the vertical error with a similar computational expense.