In many animals, response to predators occurs at greater distances the further an individual is from a refuge, but this has rarely been investigated in birds. Here, we test the hypothesis that the further from refuge (i.e. water) a foraging black swan Cygnus atratus is situated, the longer its flight initiation distance (FID) in response to a pedestrian approach on land. As predicted, swans situated farther from water exhibited longer FIDs compared with those closer to the shore. In addition, there was the possibility of an interesting interaction effect (p < 0.061) of sex and direction of approach on FID. Whilst males tended to not alter their response in relation to the angle of approach relative to the water, females tended to respond at longer distances, when approached from the shore than when approached from the land or parallel to the shore. This is one of the first reports of sex differences in FIDs for birds, with sex differences only manifesting themselves under certain approach types. Group size, the order of repeated approaches, and time of day did not influence responses, although starting distance of approach was positively related to FID.