Newton-Kantorovich method combined with moment method is applied to solve the nonlinear coulped integral equations arising from imaging of conducting object illuminated by plane waves with multiple frequencies and multiple incident directions in the paper

pseudoinverse technique based on Gram-Schedmit procedure is adopted for the solution of ill-conditioned linear equations. Least square error method（LSE） is adopted to calculate the initial values. Two techniques are also introduced to reduce the CPU time. Numerical results have shown the validity of the method and high tolerance of noise.