Lévy walks have been observed in various organisms ranging from cells, insects, fishes, and birds to mammals, including humans. However, why Lévy walks are common in biological movements remains an open question. Based on some evidence that Lévy walks are spontaneously generated in the brain, and the fact that power-law distributions in Lévy walks can emerge at a critical point, we hypothesized that the advantages of Lévy walks might result from the criticality of the brain. Here, we modeled nonlinear systems for locomotion and showed that Lévy walks emerging near a critical point had optimal dynamic ranges to environmental stimuli. We then showed that the high flexibility of Lévy walks enabled switching exploitation/exploration based on the nature of external cues. Finally, we analyzed the movement trajectories of freely moving Drosophila larvae and showed that the Lévy walks might emerge near a critical point and have a large dynamic range and high flexibility. Our results suggest that the commonly observed Lévy walks emerge near a critical point and could be explained based on these functional advantages.