Simultaneous localization and mapping (SLAM) is one of the essential techniques and functionalities used by robots to perform autonomous navigation tasks. Inspired by the rodent hippocampus, this paper presents a biologically inspired SLAM system based on a LiDAR sensor using a hippocampal model to build a cognitive map and estimate the robot pose in indoor environments. Based on the biologically inspired model, the SLAM system using point cloud data from a LiDAR sensor is capable of leveraging the self-motion cues from the LiDAR odometry and the local view cues from the LiDAR local view cells to build a cognitive map and estimate the robot pose. Experiment results show that the proposed SLAM system is highly applicable and sufficiently accurate for LiDAR-based SLAM tasks in both simulation and indoor environments.