In this paper, based on cusp catastrophic theory, the mechanical mechanism of water-inrush due to the destabilization of the key stratum of mine water-pressed floor is analyzed by using the principles of force balance and energy balance, the cusp catastrophic model of key stratum of floor is established, and the mechanical conditions of destabilization of key stratum are given out. Through the analyses of an engineering example, it is proved that it is practical to use cusp catastrophic model and numerical simulation analyze and predict the water-inrush from mine floor.