Message framing contributes to an increase in public support for invasive species management. However, little is known about people’s preferences for the multiple objectives of management within different contexts relating to the challenges and benefits of invasive species management. We examine Japanese citizens’ preferences for the goals of free-roaming unowned cat (Felis catus) management in three contextual frames by applying experimentally controlled information and the best–worst scaling technique. Our results indicate that the ecological frame highlighting the ecological impacts of free-roaming unowned cats on native ecosystems significantly increases Japanese citizens’ concern about cat predation, although the frame did not change the preference ranking of goals. There are differences in the effects of message framing depending on cat ownership. The best–worst scaling technique shows that Japanese citizens prefer to maintain a sanitary environment, followed by the prevention of zoonotic diseases. Although the ranking of sanitary environmental management does not depend on cat ownership, the ranking of the other goals differs depending on cat ownership. The findings highlight the importance of strategic message framing and its prioritization in encouraging public support for invasive species management.