Optimal foraging theory has been used to understand the foraging choices of animals but is rarely applied to large predatory fishes due to difficulties measuring their behavior in the wild. Great hammerhead sharks (Sphyrna mokarran) are atypical among sharks in that they prefer large prey, such as other sharks and large teleost species, rather than smaller teleost or invertebrate prey. Great hammerheads are known to hunt blacktip sharks (Carcharhinus limbatus) that form large seasonal aggregations off the coast of southern Florida. However, the foraging advantage of this dietary choice and hunting strategy is unclear. We equipped great hammerheads with biologging sensors (speed, video, sonar) to estimate swimming metabolic rates and prey encounter rates and then model the foraging benefits of hunting large prey (sharks) versus small prey (reef-associated teleosts). We estimate great hammerheads need to consume 0.7% body weight (BW) per day of shark prey or 0.9% BW per day of teleost prey. Our foraging model predicts that a ~ 110 kg hammerhead would only need to consume a whole ~ 25 kg blacktip shark once every 3 weeks and could survive 2 months during low blacktip density periods without feeding before starving to death. However, it would need to capture one to two ~ 1 kg teleost per day to avoid falling below its energetic baseline. Great hammerhead sharks may obtain significant benefits by hunting sharks in southern Florida, especially during the winter when prey density is high.