The spectroscopic data recorded by a dispersion spectrophotometer are usually degraded by the response function of the instrument. To improve the resolving power, double or triple cascade spectrophotometers and narrow slits have been employed, but the total flux of the radiation available decreases accordingly, resulting in a lower signal-to-noise ratio (SNR) and a longer measurement time. However, the spectral resolution can be improved by mathematically removing the effect of the instrument response function. A high-order statistical Gauss-Newton algorithm is proposed to blindly deconvolve the measured spectroscopic data. The true spectrum and the instrument response function are estimated simultaneously. Experiments on artificial and real measured spectroscopic data demonstrate the feasibility of this method.