This report is devoted to a numerical method of solution of the RFQ structure optimization problem. The problem is considered as a control theory problem. Control functions representing geometry of the electrodes and a quality functional describing the beam are introduced. To solve the problem numerically these control functions are parametrized. The presented method is based on the computation of the derivatives of the first and the second order of the quality functional on the parameters. Results of investigation of efficiency of the method relatively to a method including computation of the derivatives only of the first order are presented.