Introduced mammals pose serious threats to native island fauna, and understanding their distributionis fundamental to evaluating their conservation impact. Introduced sugar gliders (Petaurus breviceps) are the mainpredator of critically endangered swift parrots (Lathamus discolor) on mainland Tasmania. We surveyed sugar gli-der occurrence over~800 km2in an important swift parrot breeding area, the Southern Forests. During 4–5 vis-its per site, we used call broadcast of predatory owls to elicit sugar glider alarm calls and surveyed 100 sitesduring February/March 2016. Na€ıve occupancy by sugar gliders was high (0.79), as was detectability(0.520.03 SE), resulting in a cumulative detection probability of effectively 1. Occupancy modelling indicateda 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 studyrevealed 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 coverapproached 100% (i.e. in the best quality breeding habitat for swift parrots), occupancy by sugar glidersapproached 1. Our results reveal that sugar gliders are widespread across the study area which may be indicativeof occupancy rates elsewhere in the breeding range of the critically endangered swift parrot. As a result, the riskof predation by sugar gliders for small birds may be widespread across logged Tasmanian forests. Additionalwork to identify whether population densities of sugar gliders vary with forest cover (and whether this mayimpact predation likelihood) is critical to understanding the conservation consequences of deforestation in thebreeding range of the swift parrot.