Axisymmetric method is a way to use two-dimensional method to simplify three-dimensional problem. On the base of finite element method (FEM), using smoothed finite element method (S-FEM) to analyze axisymmetric elements is a method to improve the calculation accuracy. In this paper, an edge based smoothed finite element method (ES-FEM) which is the most accurate method in S-FEM is analyzed for axisymmetric problems. The most important part in axisymmetric problems is the calculation of strain matrix. Different from simple average in most FEM, we combine geometric analytical calculations with smoothing technique when calculating the strain matrix. The geometric analytical calculations can accurately calculate the n-th moment of the polygon through formulas. Therefore, this method can achieve the integration of the shape function while avoiding mapping and calculation of Jacobian matrix. Numerical examples are analyzed to verify the reliability of the methods. All the calculations of numerical examples are implemented in ABAQUS by using the user-defined element library (UEL). It broke the restriction that UEL can only use one element to embed. Therefore, it improves the efficiency of simulation. And the results of the numerical examples show that the new method has good performance in axisymmetric problems.