To reduce the influence of stray lights on the spectral measurement accuracy of a High Resolution Imaging Spectrometer(HRIS), sources and hazards of stray lights were analyzed. Based on the Point Spread Function (PSF) theory which is usually used to describe the stray lights of HRISs,the influence matrix and the correction matrix of stray lights were discussed. The measurements and specific correction programs were given, and the accuracies of measurement and correction were analysed. The results show that the method based on PSF can complete the measurement and correction of stray lights for the HRIS. For a pixel center wavelength incident light, the effective signal is only reduced no more than 1%, while the stray light signal is reduced at least by 99% as compared with the raw data. For both pixel center wavelength and non-pixel center wavelength incident lights, the corrected signals are reduced by about 7% at the pixel center wavelength and by nearly 25% at the non-pixel center wavelength, while the stray light signal is reduced by almost 50%. Finally, the theoretical reasons why the incident light wavelength affected the stray light correction were explained.