3D object detection has achieved significant performance in many fields, e.g., robotics system, autonomous driving, and augmented reality. However, most existing methods could cause catastrophic forgetting of old classes when performing on the class-incremental scenarios. Meanwhile, the current class-incremental 3D object detection methods neglect the relationships between the object localization information and category semantic information and assume all the knowledge of old model is reliable. To address the above challenge, we present a novel Incremental 3D Object Detection framework with the guidance of prompting, i.e., I3DOD. Specifically, we propose a task-shared prompts mechanism to learn the matching relationships between the object localization information and category semantic information. After training on the current task, these prompts will be stored in our prompt pool, and perform the relationship of old classes in the next task. Moreover, we design a reliable distillation strategy to transfer knowledge from two aspects: a reliable dynamic distillation is developed to filter out the negative knowledge and transfer the reliable 3D knowledge to new detection model; the relation feature is proposed to capture the responses relation in feature space and protect plasticity of the model when learning novel 3D classes. To the end, we conduct comprehensive experiments on two benchmark datasets and our method outperforms the state-of-the-art object detection methods by 0.6% - 2.7% in terms of mAP@0.25.