The greater bilby (Macrotis lagotis) is the sole remaining species of desert bandicoot on the Australian mainland. The mating system of this species remains poorly understood, due to the bilby’s cryptic nature. We investigated the genetic mating system of the greater bilby in a five-year study of a semi-free-ranging captive population that simulated their wild environment. Morphological traits were examined to determine whether these influenced patterns of male reproductive success and whether selection was acting on them. In any given year more than half the males (59.2 ± 9.3%) failed to sire any offspring. Approximately 70% of sires fathered one offspring, and 30% two or three offspring. Since paternity was not dominated by few males, and given the species’ solitary nature, lack of territoriality and large home ranges, it is likely that males adopt a roving strategy to find receptive females. These results are consistent with an overlap promiscuous mating system. Sires and non-sires could not be distinguished by their morphological traits, and there was no evidence for strong linear or non-linear selection on male traits. These data increase our understanding of bandicoot life-history traits and will assist conservation and management efforts.