A new method for the reconstruction of one dimensional profile of a perfectly conducting rough surface is presented. The method is based on the equivalent representation of the rough surface by means of an inhomogeneous impedance plane, whose surface impedance is recovered through the analytical continuation of the measured data. The equivalent problem allows one to calculate the total field in the whole space above the unknown surface. The use of boundary condition that the total electric field vanishes on the unknown surface enables to reduce the problem to the solution of a non-linear equation in terms of the unknown surface function. The non-linear equation is solved iteratively via Newton method and regularization in the least square sense is also applied. The effectiveness of the method has been demonstrated with several numerical simulations.