A new method to measure the spectrum of a pulse light was developed. As the pulse width could be broaden due to the dispersion when a pulse light passed through the optical fiber, the calibration and measurement were proposed to correct and recover the broaden waveform to obtain the real spectrum of a pulse light source. In calibration, the time response function of measuring system was gotten with a ps laser firstly; then the group refractive indexes at different wavelengths were obtained by measuring the time delay of given wavelengths; finally, the relative attenuation index of each wavelength in optical fiber was given by measuring the spectral attenuation. On the basis of the calibration results mentioned above, broaden waveform was recovered by the digital deconvolution, time delay and attenuation .The pulse spectrum of a red scintillator was measured with this method. Results demonstrate that the difference of the center wavelength of the scintillator given by this method and other methods is less than 2 nm, which shows the spectra of pulse light can be measured based on fiber dispersion when the pulse width is much less than its dispersion.