This paper describes a neural model for a robot learning spatial knowledge and navigating on learned place and head-direction (HD) cell representations. The place and HD cells, which are trained through unsupervised slow feature analysis (SFA) from sequences of visual stimuli, provide positional and directional information for navigation. Based on the ensemble activity of place cells, the robot learns a topological map of the environment through extracting the statistical distribution of the place cell activities covering the traversable areas and realizes self-localization based on the map. The robot's heading direction, which is encoded by the HD cells, works as a control signal to adjust its behavior. Action representations supporting state transitions are learned through memorizing the same movement from a previous phase where an experimenter drives a robot to explore an environment. Given reward signals spreading from a target location along the topological map, the robot can reach the goal in a reward-ascending way. This work intends to build a practical navigation system by simulating animals' hippocampal cell firing activities on a robot platform using its self-contained sensor. Experimental results from simulation demonstrate that our system navigates a robot to the desired position smoothly and effectively.