The spectroscopic data recorded by dispersion spectrophotometer are usually degraded by the response function of the instrument. To improve the resolving power, double or triple cascade spectrophotometer and narrow slits have been employed, but the total flux of the radiation decreases accordingly, resulting in a lower signal-to-noise ratio (SNR) and a longer measuring time. However, the spectral resolution can be improved by mathematically removing the effect of the instrument response function. Based on the Shalvi-Weinstein criterion, a Gauss-Newton based kurtosis blind deconvolution algorithm for spectroscopic data is proposed. Experiments with some real measured Raman spectroscopic data show that this algorithm has excellent deconvolution capability.