Based on the theoretical foundation of lower bound limit analysis method, corresponding equilibrium equation is derived by using complete stress field of slope which has been built based on perfectly pin connected truss assumption. Catastrophe model of slope failure is constructed based on mutation feature of slope failure. System model property and slope failure mechanism are analyzed, and the lower bound solution of slope failure is achieved. Ultimate load of a slope example is analyzed, and comparison between the solution acquired by the proposed method and the classical plastic theory and comparison between the solution acquired by the proposed method and the finite element method are adopted to illustrate the feasibility of the proposed method. The key difficult problem of slope lower limit analysis is solved by using the catastrophe theory. The executive idea of this research may provide a new optional approach to solve lower bound theoretical solution of ultimate bearing capacity of slope.