The across-track illumination variation in Earth Observing-1 (EO1) Hyperion images is a result of wavelength-shift and full-width-at-half-maximum (FWHM)-shift in the cross-track direction. Correction in across-track illumination variation is necessary for accurate spectral matching and classification. This contribution reviews the available methods for the correction of across-track illumination variation, and evaluates them for correcting a Hyperion image of study area around the Udaipur city in western India. We also describe and demonstrated a new technique for correcting these artefacts. For each band, the spatial trends of (a) nonlinear shifts in the nominal centre wavelengths of bands across the image columns and (b) nonlinear changes in the nominal FWHM of bands across the image columns are modelled using quadratic regression and are compensated using a radiance correction factor estimated from the columns characterized by minimum illumination variations in a spectrally flat area of the image. A series of statistical measures, spectral matching, minimum noise fraction transform (MNF) images, and post-correction classification results were used to evaluate the performance of the proposed algorithm vis-a-vis some of the previous methods on the Hyperion image of the study area. The results indicate that the proposed method effectively corrects the across-track illumination effects in the Hyperion image of the study area, and also show better performance in lithological as well as for land-use and land-cover mapping, as compared to the other previous methods.