Obtaining cooperation from the local people is a key factor in an efficient management of invasive species. However, conflicts between invasive species managers and local people occur, when the target species is strongly bonded with humans. To understand the attitudes and behaviors of local people toward the issues on free-roaming cats ( Felis silvestris catus ), we conducted a questionnaire study covering all high school students—who are important future stakeholders and could reflect ideas of their parents whose responses are hard to attain—on Tokunoshima Island, Japan, where the ecological negative impacts of free-roaming cats are exacerbated by residents’ feeding. We used a cognitive hierarchy model and structural equation modeling (SEM) to study the relations between our questionnaire items: background characteristics (i.e., cat ownership, education experience around cat-caused negative ecological impacts, attitudes and perceptions around cats and nature), perceptions of the negative cat impacts on nature and people, attitudes toward outdoor cat management, and the frequency of outdoor feeding. Results from 1162 youth respondents showed that cat owners and people who believed that cats are useful for rodent control exhibited a higher frequency of outdoor feeding, perhaps due to feeding their own cats outdoors. Perceptions on the negative impacts of cats on people (e.g., zoonoses and public nuisances) which were disagreed by cat lovers, showed a stronger effect than the perceptions of negative ecological impacts, in terms of the approval of outdoor cat management. In general, informing people about the threats of outdoor cats to people, house-owned cats and livestock through education activities regarding the cat issues will lead to a better understanding and cooperation toward outdoor cat management. Educating teenagers who are more likely to accept new knowledge is especially necessary. Keeping cats indoors and reducing the frequency of feeding outdoor cats are still one of the fundamental solutions to decrease the number of outdoor cats, which will in turn decrease the risk of cat predation on native species.