The problem of phase function reconstructing in Hilbert diagnostics of gaseous, condensed and reacting media is discussed in the work. The method for reconstructing the phase disturbances structure of a probing light field, based on the iterative Gauss-Newton al- gorithm, is proposed.This method does not require the second derivatives determination and greatly reduces the number of calculations.It consists in the sequential selection of a complex phase profile, which is specified by the sum of third degree Bezier curves, and the hilbertogram calculation in order to minimize the root-mean-square error between the experimental and reconstructed hilbertograms. The Jacobi matrix for the nonlinear integral operator of Hilbert visualization is calculated. The proposed algorithm was tested on test functions.The devel- opment of the method and its applications is associated with the application of the algorithm to the processing of experimental results.