Encounter rates of carnivores with prey are dependent on spatial and temporal overlap, and are often highest with their preferred prey. The Critically Endangered Sumatran tiger Panthera tigris sumatrae is dependent on prey populations, but little is known about its prey preferences. We collected camera-trap data for 7 years (2010–2016) in Bukit Barisan Selatan National Park, Sumatra, to investigate spatial and temporal overlap of tigers with potential prey species. We also developed a novel method to predict predator–prey encounter rates and potential prey preferences from camera-trap data. We documented at least 10 individual tigers, with an overall detection rate of 0.24 detections/100 trap nights. Tigers exhibited a diurnal activity pattern and had highest temporal overlap with wild boar Sus scrofa and pig-tailed macaques Macaca nemestrina, but highest spatial overlap with wild boar and sambar deer Rusa unicolor. We created a spatial and temporal composite score and three additional composite scores with adjustments for the spatial overlap and preferred prey mass. Wild boars ranked highest for all composite scores, followed by sambar deer, and both are known as preferred tiger prey in other areas. Spatial and temporal overlaps are often considered as separate indices, but a composite score may facilitate better predictions of encounter rates and potential prey preferences. Our findings suggest that prey management efforts in this area should focus on wild boar and sambar deer, to ensure a robust prey base for this Critically Endangered tiger population.