In diploids, F1 offspring performance is expected to increase with increasing genetic dissimilarity between the parents until an optimum is reached because outbreeding mitigates inbreeding depression and maximizes heterosis. However, many flowering plant species are derived through allopolyploidization, i.e. interspecific hybridization with genome doubling. This mode of plant speciation can be expected to considerably alter the consequences of inbreeding and outbreeding. We investigated the F1 fitness consequences of mating over a range of (genetic) distances in the allohexaploid plant species Geum urbanum. Offspring was raised under controlled conditions (632 plants). The performance of outcrossed progeny was not significantly better than that of their selfed half-siblings and did not increase with parental genetic dissimilarity (0–0.83). Our findings support low, if any, inbreeding depression and heterosis. We attribute this to the peculiar state of quasi-permanent heterozygosity in allopolyploids and frequent selfing.