Introduced mammals pose serious threats to native island fauna, and understanding their distribution is fundamental to evaluating their conservation impact. Introduced sugar gliders (Petaurus breviceps) are the main predator of critically endangered swift parrots (Lathamus discolor) on mainland Tasmania. We surveyed sugar glider occurrence over ~800 km2 in an important swift parrot breeding area, the Southern Forests. During 4–5 visits per site, we used call broadcast of predatory owls to elicit sugar glider alarm calls and surveyed 100 sites during February/March 2016. Natıve occupancy by sugar gliders was high (0.79), as was detectability (0.52 0.03 SE), resulting in a cumulative detection probability of effectively 1. Occupancy modelling indicated a positive effect of the proportion of mature forest cover on occupancy. The best model, based on AIC scores, included the proportion of mature forest cover within a 500 m radius with constant detectability. Our study revealed surprisingly high rates of occupancy of available forest habitat throughout the heavily logged study area, such that even when mature forest cover was <10%, sugar glider occupancy was >0.5; where forest cover approached 100% (i.e. in the best quality breeding habitat for swift parrots), occupancy by sugar gliders approached 1. Our results reveal that sugar gliders are widespread across the study area which may be indicative of occupancy rates elsewhere in the breeding range of the critically endangered swift parrot. As a result, the risk of predation by sugar gliders for small birds may be widespread across logged Tasmanian forests. Additional work to identify whether population densities of sugar gliders vary with forest cover (and whether this may impact predation likelihood) is critical to understanding the conservation consequences of deforestation in the breeding range of the swift parrot.