Invasive species pose a serious threat to native species. In Europe, invasive grey squirrels (Sciurus carolinensis) have replaced native red squirrels (Sciurus vulgaris) in locations across Britain, Ireland and Italy. The European pine marten (Martes martes) can reverse the replacement of red squirrels by grey squirrels, but the underlying mechanism of how pine martens suppress grey squirrels is little understood. Research suggests the reversal process is driven by direct predation, but why the native red squirrel may be less susceptible than the invasive grey squirrel to predation by a commonly shared native predator, is unknown. A behavioural difference may exist with the native sciurid being more effective at avoiding predation by the pine marten with which they have a shared evolutionary history. In mammals, olfactory cues are used by prey species to avoid predators. To test whether anti-predator responses differ between the native red squirrel and the invasive grey squirrel, we exposed both species to scent cues of a shared native predator and quantified the responses of the two squirrel species. Red squirrels responded to pine marten scent by avoiding the feeder, increasing their vigilance and decreasing their feeding activity. By contrast, grey squirrels did not show any anti-predator behaviours in response to the scent of pine marten. Thus, differences in behavioural responses to a shared native predator may assist in explaining differing outcomes of species interactions between native and invasive prey species depending on the presence, abundance and exposure to native predators.