X chromosome meiotic drive (XCMD) kills Y‐bearing sperm during spermatogenesis, leading to the biased transmission of the selfish X chromosome. Despite this strong transmission, some natural XCMD systems remain at low and stable frequencies, rather than rapidly spreading through populations. The reason may be that male carriers can have reduced fitness, as they lose half of their sperm, only produce daughters, and may carry deleterious alleles associated with XCMD. Thus, females may benefit from avoiding mating with male carriers, yielding a further reduction in fitness. Genetic suppressors of XCMD, which block the killing of Y sperm and restore fair Mendelian inheritance, are also common and could prevent the spread of XCMD. However, whether suppressed males are as fit as a wild‐type male remains an open question, as the effect that genetic suppressors may have on a male's mating success is rarely considered. Here, we investigate the mating ability of XCMD males and suppressed XCMD males in comparison to wild‐type males in the fruit fly Drosophila subobscura, where drive remains at a stable frequency of 20% in wild populations where it occurs. We use both competitive and non‐competitive mating trials to evaluate male mating success in this system. We found no evidence that unsuppressed XCMD males were discriminated against. Remarkably, however, their suppressed XCMD counterparts had a higher male mating success compared to wild‐type controls. Unsuppressed XCMD males suffered 12% lower offspring production in comparison to wild‐type males. This cost appears too weak to counter the transmission advantage of XCMD, and thus the factors preventing the spread of XCMD remain unclear.