Abstract: The coal rock energy model is established in order to analyze the factor that causes the outburst of coal and gas, and then the cusp catastrophe models of coal and gas outburst are established by using mutation theory. The process of coal and gas outburst is elaborated based on analyzing variable quantity to the mutation control of catastrophe. The potential anamorphic energy of coal, the inner energy of firedamp, the broking energy of coal, and the movement energy of broken coal play vital roles in deciding whether the coal and gas will burst out or not. If the soft layer of coal exists in the coal seams, the broking energy of coal is relatively small, so it is prone to the outburst of coal and gas under the same conditions. The research results have important denotation for the disaster prediction and prevention of coal and gas outburst.