The theory of synchrotron radiation (SR) has been well understood and published. We study the numerical methods for the reconstruction of the spectral distribution function of SR by measurement of the attenuation of the SR energy spectrum. The reconstruction of the spectral distribution function of SR is an ill-posed integral operator equation of the first kind. Therefore, how to overcome the ill-posedness is a major task in numerical computation. We study the projected gradient methods and propose a non-monotone decreasing algorithm, which is called the projected Barzilai-Borwein (PBB) method. The feasibility of the method is studied in detail by using a hypothetical SR spectrum. The applied results of the spectrum of 4W1B beamline (an unfocused X-ray monochromator beamline with 4 mrad (milliradian) of horizontal acceptance which is extracted from the wavelength shifter 4W1) in BSRF (Beijing Synchrotron Radiation Facility) are shown.