A large brain can offer several cognitive advantages. However, brain tissue has an especially high metabolic rate. Thus, evolving an enlarged brain requires either a decrease in other energetic requirements, or an increase in overall energy consumption. Previous studies have found conflicting evidence for these hypotheses, leaving the metabolic costs and constraints in the evolution of increased encephalization unclear. Mormyrid electric fishes have extreme encephalization comparable to that of primates. Here, we show that brain size varies widely among mormyrid species, and that there is little evidence for a trade-off with organ size, but instead a correlation between brain size and resting oxygen consumption rate. Additionally, we show that increased brain size correlates with decreased hypoxia tolerance. Our data thus provide a non-mammalian example of extreme encephalization that is accommodated by an increase in overall energy consumption. Previous studies have found energetic trade-offs with variation in brain size in taxa that have not experienced extreme encephalization comparable with that of primates and mormyrids. Therefore, we suggest that energetic trade-offs can only explain the evolution of moderate increases in brain size, and that the energetic requirements of extreme encephalization may necessitate increased overall energy investment.