The spatial resolution of hyperspectral imaging systems is constrained by a spatial-spectral resolution tradeoff and current technique limitations. However, spatial resolution is a critical feature for applications that require high spatial resolution and utilization of details. We present a method of restoring high-resolution (HR) images from a set of low-resolution (LR) hyperspectral data cubes with subpixel shifts across different bands. A new observation model is introduced to demonstrate LR hyperspectral images at different bands and an HR image that covers all these bands. A regularized super-resolution (SR) algorithm is then implemented to solve the problem. Experiments of the proposed algorithm and existing SR algorithms are performed and the results are evaluated. The results demonstrate the feasibility of the proposed SR method. Moreover, the image fusion results also demonstrate that the restored image is suitable for enhancing the spatial resolution of entire hyperspectral data cubes.