Abstract: Based on the calculated results of finite element method,the problem of slope stability could be converted into searching for the shortest path in graph theory.A new method of slope stability,limit equilibrium finite element method based on Dijkstra algorithm,was established by applying the improved Dijkstra algorithm which was an algorithm to seek the shortest path in graph theory to search for the minimum safety factor of slopes and the position of most dangerous sliding plane.A classical slope case was specialized to validate this method.The safety factor of slopes and the position of most dangerous sliding plane according to this method were basically consistent with the propositional answer so its feasibility was proved.This method was applied in the stability analysis for the slope of the outlet of the flood discharge tunnel in the right bank of Nuozhadu Hydropower Station.It was shown that the safety factor of slopes from this method was between that of the limit equilibrium method and that of the strength reduction method,and the position of dangerous sliding plane was basically consistent with that of these two methods.This method could be applied in the stability analysis of complicated rock slopes.Finally,with regard to the sliding surface developing opposite to the slope direction,it was illustrated how to compute the stress of the sliding surface through an example in the stability analysis of the right bank slope in Luogu Hydropower Station.Comparson between the computed results of 3DEC and those of this method shows that the present method is suitable for the stability analysis of the sliding surface developing opposite to the slope direction.