The present paper introduces the stray light and bandpass correction methods for spectrometers. The line spread function of spectrometer is characterized by a He-Ne laser. Assuming that the spectrometer is a wavelength invariable system, the stray light distribution matrix is constructed by the derived line spread functions. The stray light correction matrix is then derived by matrix conversion from the stray light distribution matrix. The measured signals of the spectrometer are finally multiplied by the stray light correction matrix to correct the stray light errors. The bandpass functions of the spectrometer are characterized in three different wavelength ranges, respectively. And then three groups of bandpass correction coefficients are calculated accordingly. The calculation is divided into several steps. Given the measurement results at the target wavelength position and the ones on the neighbor bandwidths, the bandpass correction results are obtained by weight averaging of them. The bandpass correction coefficients are used as the weights. The two correction methods are applied to a multi-channel fast spectrometer to measure LEDs of different color. The results show that the stray light and the bandpass errors can be corrected effectively. The chromaticity coordinates of the LEDs are corrected by (-0.003, 0.007) for the maximum. Furthermore, the method introduced in this paper can reduce the application cost, simplify the calculation under a reasonable precision, and make the application of the correction easier.