Adversarial attacks have been recently investigated in LiDAR perception problems for autonomous driving, where a small perturbation of source inputs can result in incorrect predictions. However, most previous studies focus on attacks on single-frame perception modules, lacking explorations of attacks on consecutive-frame tasks, i.e. the LiDAR odometry. In this paper, we propose a gradient optimization-based adversarial attack towards deep LiDAR odometry networks. To generate point clouds consistent with real-world scenarios, we constrain adversarial points within the range of a small object, e.g. a traffic cone, and render new points to simulate real LiDAR measurements. By incorporating such adversarial points in consecutive frames, we demonstrate a significant decrease in pose estimation accuracy of current popular LiDAR odometry networks. In addition, we also evaluate traditional geometric odometry approaches and report their robustness against adversarial points. Extensive experiments on the KITTI and Waymo datasets illustrate the effectiveness of the proposed attack method and the vulnerability of deep LiDAR odometry networks against adversarial points.