In this paper, we present the first application of the Generalized Gaussian Markov Random Field (GGMRF) to the problem of video super-resolution. The GGMRF prior is employed to perform a maximum a posteriori (MAP) estimation of the desired high-resolution image. Compared with traditional prior models, the GGMRF can describe the distribution of the high-resolution image much better and can also preserve better the discontinuities (edges) of the original image. Previous work had used GGMRF for image restoration in which the temporal dependencies among video frames are not considered. Since the corresponding energy function is convex, gradient descent optimisation techniques are used to solve the MAP estimation. Results show the super-resolved images using the GGMRF prior not only offers a good visual quality enhancement, but also contain a significantly smaller amount of noise.