A novel method is proposed to measure spectrum with waveguide holographic grating, based on fast Fourier transform for the interference pattern from the diffraction of light through the side of a fiber grating. The range of measurable optical wavelengths and resolvable wavelength interval are discussed with considering the period length of waveguide holographic grating and parameters of CCD detector. This method of spectrum measurement has the advantages of high resolution of spectrum, wide wavelength scope and simple structure etc.