The fiducial marker system for LiDAR is crucial for the robotic application but it is still rare to date. In this letter, an Intensity Image-based LiDAR Fiducial Marker (IILFM) system is developed. This system only requires an unstructured point cloud with intensity as the input and it has no restriction on marker placement and shape. A marker detection method that locates the predefined 3D fiducials in the point cloud through the intensity image is introduced. Then, an approach that utilizes the detected 3D fiducials to estimate the LiDAR 6-DOF pose that describes the transmission from the world coordinate system to the LiDAR coordinate system is developed. Moreover, all these processes run in real-time (approx 40 Hz on Livox Mid-40 and approx 143 Hz on VLP-16). Qualitative and quantitative experiments are conducted to demonstrate that the proposed system has similar convenience and accuracy as the conventional visual fiducial marker system.