A simple, practical method has been developed to correct a spectroradiometer's response for measurement errors arising from the instrument's spectral stray light. By characterizing the instrument's response to a set of monochromatic laser sources that cover the instrument's spectral range, one obtains a spectral stray light signal distribution matrix that quantifies the magnitude of the spectral stray light signal within the instrument. By use of these data, a spectral stray light correction matrix is derived and the instrument's response can be corrected with a simple matrix multiplication. The method has been implemented and validated with a commercial CCD-array spectrograph. Spectral stray light errors after the correction was applied were reduced by 1-2 orders of magnitude to a level of approximately 10(-5) for a broadband source measurement, equivalent to less than one count of the 15-bit-resolution instrument. This method is fast enough to be integrated into an instrument's software to perform real-time corrections with minimal effect on acquisition speed. Using instruments that have been corrected for spectral stray light, we expect significant reductions in overall measurement uncertainties in many applications in which spectrometers are commonly used, including radiometry, colorimetry, photometry, and biotechnology.