The methods of specification, analysis and evaluation on telescope primary mirror figure error have an important instructive meaning to mirror fabrication. A structure function analysis method is introduced. Firstly, the influence of atmospheric turbulence on image quality is analyzed and the specification on mirror figure error is determined using the structure function analysis method. Then the evaluation on mirror figure error and the guidance of mirror processing by conversion from Zernike polynomial to structure function are achieved. The conversion processes and results have been described. Finally, the analysis processes mentioned above are illustrated in detail by an example of Giant Magellan Telescope (GMT). The structure function analysis method which has a greater guiding significance can evaluate the mirror figure error accurately and perfectly and shows advantages over the root-mean-square (RMS) wave aberration method.