The two - dimensional ( 2D) boundary value problem of the complex shape boundary is solved by combing the Green's function method and conformal mapping. Meanwhile the distribution of electric field is got.Both the electric field line and equipotential line maps are plotted by using mathematical software MATLAB，thus the validity of the method in the paper is presented. The application range for the Green's function method is expanded，and a novel idea and way is provided for solving the complex shape boundary 2D electrostatic field boundary value problem.