Abstract: This paper explores the parabolic equations involving fractional Monge-Ampère operator. Firstly, by constructing a suitable subsolution and contradiction, Hopf’s lemma for parabolic equations involving fractional Monge-Ampère operator is investigated. Secondly, by asymptotic analysis of the parabolic equations involving fractional Monge-Ampère operator, asymptotic Hopf’s lemma for antisymmetric functions is proved.