Punitive damages are combined with penalty in the field of criminal with civil public interest litigation, which can adapt to the nature of criminal acts, effectively promote the complementary of criminal and civil responsibilities, and achieve double punishment. But the difficulty in connecting punitive damages and penalty lies in the difference in the subjective elements as “intention”. For the first time, the “Civil Code” clearly stipulated the subjective element of punitive damages for environmental tort as “intention”. This “intention” is different from criminal intention because it includes not only the actual knowledge of the result, but also the potential or expected knowledge of the result, and it has no cognitive requirements on the substance of criminal acts. This difference is rooted in the fundamental difference in the legitimacy of criminal liability and punitive damages, and the connection between criminal intention and punitive damages intention should be realized on the basis of facing the difference, then promote the rational connection of the identification of elements and realize the protection and relief of the public interests of the society.