The giant perilous rock at Wangxia (named Wangxia perilous rock) is representative in Three Gorges of the Yangtze River, China, has threatened badly the navigation of the Yangtze River channel for a long period. The giant perilous rock is composed of siliceous limestone and argillaceous limestone, and includes two elements marking by W1 and W2, respectively. The W1 is an isolated pillar while the W2 is in clintheriform. The linking segment of dominant fissure in the W2 is composed by moniliform solution funnels at its back, and the locked segment of the dominant fissure at the base of the W2 is composed by two parts. For the locked part of the dominant fissure of the W2, the upper segment shows the same lithology with the perilous rock and it can be simplified as an elastic medium, for the lower segment composed by argillaceous shale and mudstone can be simplified as a strain-softening medium. Introducing the water-softened function, the constitutive curves with two kinds of medium materials for the locked segment in the dominant fissure of the W2 have been proposed. Based on energy principle, the cusp catastrophe model for perilous rock rupture is built and formulas for the transient elastic and impulsive acceleration and the elastic-impulsive velocity of perilous rock catastrophe rupture have been established. By the calculation, the elastic-impulsive acceleration for the catastrophe rupture of the W2 is 531.4 m/s2, while the average elastic-impulsive velocity is 2.608 m/s. Further, it is deduced that the elastic-impulsive velocity at the base of the W2 is about 5.2 m/s. For the transient ruture of the W2, there is a greater speed difference between the top and the base of the W2, which impels the giant perilous rock to be retroverted sliding rupture, coinciding with the fact. Undoubtedly, studies in this paper must play an important role to analyze the catastrophe rupture mechanism of giant perilous rocks at both banks in Three Gorges of the Yangtze River, China.