Entorhinal grid cells are characterized by spatially periodic patterns of activity and have been suggested to provide a metric of space. However, environmental geometry distorts grid-cell firing patterns in highly polarized trapezoidal compared to less polarized square environments. Here, we address the question whether human spatial cognition is influenced by these distortions of grid-cell firing patterns. Participants navigated a trapezoidal and a square arena using immersive virtual reality while learning the positions of objects. Positional memory was degraded in the trapezoid compared to the square. Following the distortions of grid-cell firing patterns in rodents, this effect was more pronounced in the narrow compared to the broad part of the trapezoid. Further, identical distances between object pairs were estimated to be different between the two parts of the trapezoid. These findings suggest that distortions of grid-cell firing patterns impact cognitive functions beyond spatial navigation.