Abstract: In the problem of linear elasticity of variable stiffness beam, the solution of the deflection curve of static load is usually obtained by integral method or unit-load method. Based on the differential equation of the problem, this paper gives a new type of solution with Green function method to get the deflection curve of the variable stiffness beam. It can be seen from the derivation results that the formulas proposed in this paper have the characteristics of uniformity, accuracy, simplicity and suitable for computerization, which will have important application value for the analysis of the frame structure.