Grid cells and place cells have shown to play an important role in spatial cognition in rats. While place cells provide global localization from external environment information, grid cells provide a “neural odometry” for path integration from internal vestibular information. In this paper we describe a spatial cognition model integrating grid cells and place cells from behavioral and neurophysiological brain studies in rats. Grid cell firing is generated from a linear oscillatory interference model that includes a reset mechanism to overcome errors in “neural odometry” readings. The model is evaluated in simulation. Future work is discussed including extensions to the model and evaluation under physical robots.