Based on the theoretical analysis, the transmission spectrum of a broadband fiber Bragg grating (FBG) have been measured by applying a passive wavelength demodulation system , in which a fiber Bragg grating wavelength scanning laser source is used. The FWHM and the peak reflectivity of the FBG to be measured is 0.48～nm and 94%, respectivly. The experiment result is in good agreement with that measured by an optical spectrum analyzer, with experimental error less than 5%.