In order to improve the efficiency and accuracy of piezoelectric structure design, the static electro-mechanical coupling of two-dimensional piezoelectric material problems are investigated by a cell-based smoothed isogeometric analysis method (CS-IGA) in this work. CS-IGA was developed on the basis of the isogeometric finite element method (IGA) by using strain smoothing technology. Based on the generalized Galerkin weak form and the constitutive equation of piezoelectric structures, the equilibrium equation of piezoelectric material in the problem of electro-mechanical coupling is obtained. In order to further improve the calculation accuracy of the algorithm, average strain is defined in the element sub-domains, which completely avoids the gradient calculation of rational NURBS basis function in the stiffness matrix formula. It also further improves the computational efficiency. Besides, numerical example results are given to verify the accuracy, convergence and correctness of the proposed method compared with the traditional finite element method (FEM) in the analysis of piezoelectric material problems. Overall, this article can provide a reference for the design and analysis of piezoelectric structure.