Consider numerical realization of Dirichlet-to-Neumann map for the Helmholtz equation with mixed boundary condition. By applying boundary integral equation (BIE) method and potential theory, the solvability of this mixed boundary value problem and an efficient method for solving the boundary Neumann date are set up. The regularization scheme for determining this D-to-N map from the measured nonsmooth Dirichlet boundary date is also given. Numerical schemes for solving BIE with singular kernel are proposed and computational results are given to show the validity of our method.