Super-resolution (SR) as a postprocessing technique is quite useful in enhancing the spatial resolution of hyperspectral (HS) images without affecting its spectral resolution. We present an approach to increase the spatial resolution of HS images by making use of sparse representation and Gabor prior. The low-resolution HS observations consisting of large number of bands are represented as a linear combination of a small number of basis images using principal component analysis (PCA), and the significant components are used in our work. We first obtain initial estimates of SR on this reduced dimension by using compressive sensing-based method. Since SR is an ill-posed problem, the final solution is obtained by using a regularization framework. The novelty of our approach lies in: (1) estimation of optimal point spread function in the form of decimation matrix, and (2) using a new prior called “Gabor prior” to super-resolve the significant PCA components. Experiments are conducted on two different HS datasets namely, 31-band natural HS image set collected under controlled laboratory environment and a set of 224-band real HS images collected by airborne visible/infrared imaging spectrometer remote sensing sensor. Visual inspections and quantitative comparison confirm that our method enhances spatial information without introducing significant spectral distortion. Our conclusions include: (1) incorporate the sensor characteristics in the form of estimated decimation matrix for SR, and (2) preserve various frequencies in super-resolved image by making use of Gabor prior.