In humans, individual and sex differences have been long reported for several cognitive tasks and are at least in part due to variability in the function that inhibits behaviour (i.e. inhibitory control). Similar evidence of individual and sex differences in inhibitory abilities is also present in other vertebrates, but is scarce outside primates. Experiments on reversal learning, which requires inhibiting behaviours, suggest that this variability may exist in a teleost fish, the guppy, Poecilia reticulata. We tested this hypothesis by observing guppies in an inhibitory task. Guppies were exposed to unreachable prey inside a transparent tube for six trials. Guppies showed a marked reduction in the number of attempts to catch the prey within the first trial and also over repeated trials. We found a striking sex difference in the capacity to inhibit foraging behaviour. Males attempted to attack the prey twice as often as females and showed negligible improvement over trials. Irrespective of sex, individuals remarkably differed in their performance, with some guppies being systematically more skilled than others across the repeated trials. These results confirm that individual and sex differences in the ability to inhibit behaviour are not restricted to humans and other primates, suggesting that they might be widespread among vertebrates. Variability in inhibitory ability provides an explanation for emerging records of variability in other cognitive tasks in fish.