Based on the theory of limit analysis, with the slope fan-shaped slice method, this paper utilized the sequential quadratic programming optimization algorithm and introduced the energy dissipation coefficient between fans to study the shape and stability of fracture surfaces of potentially unstable slopes under earthquake. This method proved to be feasible compared with an example analysis result and some similar research results. The result shows that, using this method, the potential slope fracture surface is between the straight line and the logarithmic spiral fracture surface.