Differences among males in their success in achieving fertilisations when females mate with more than one partner are now recognised as an important target of sexual selection. However, very few studies have attempted to determine whether particular males are consistently successful in sperm competition and whether success in sperm competition is a heritable trait. Additionally, the potential heritability of female traits that influence the outcome of sperm competition has received only limited attention. Using the polyandrous beetle Tribolium castaneum, we examined repeatability of male success in sperm competition by mating pairs of males carrying different visible genetic markers to a string of different females. Males showed consistency in their ability to successfully transfer sperm to females, but not in their success in sperm competition. Furthermore, when we independently compared success in sperm competition of fathers with their sons, we found no evidence for heritability of this trait. Similarly, females that exhibited high or low first male sperm precedence did not tend to have daughters that showed the same pattern. Our results suggest that we should be wary of assuming that success in sperm competition is heritable through either sex.