Abstract: Based on the basic principle of variational method and limit equilibrium method， the stability of soil slope under earthquake action is analyzed accurately. Combining the limit equilibrium method of slope stability analysis and the pseudo-static method， the auxiliary functional under constraint conditions is constructed by introducing Lagrange multiplier into the equilibrium equation of sliding soil. The first order ordinary differential equations with the basic unknowns of potential sliding surface， normal stress of sliding surface， force of sliding body， safety factor and Lagrange multiplier are obtained by using Euler equation. The coupled nonlinear differential equations are solved numerically by using the shooting method， and an accurate solution for slope stability analysis under seismic action is obtained. The effectiveness of the model and method is verified by numerical examples.