Evidence of sex differences in spatial cognition have been reported in a wide range of vertebrate species. Several evolutionary hypotheses have been proposed to explain these differences. The one best supported is the range size hypothesis that links spatial ability to range size. Our study aimed to determine whether male cuttlefish (Sepia officinalis; cephalopod mollusc) range over a larger area than females and whether this difference is associated with a cognitive dimorphism in orientation abilities. First, we assessed the distance travelled by sexually immature and mature cuttlefish of both sexes when placed in an open field (test 1). Second, cuttlefish were trained to solve a spatial task in a T-maze, and the spatial strategy preferentially used (right/left turn or visual cues) was determined (test 2). Our results showed that sexually mature males travelled a longer distance in test 1, and were more likely to use visual cues to orient in test 2, compared with the other three groups. This paper demonstrates for the first time a cognitive dimorphism between sexes in an invertebrate. The data conform to the predictions of the range size hypothesis. Comparative studies with other invertebrate species might lead to a better understanding of the evolution of cognitive dimorphism.