X-Ray fluorescence (XRF) scanning of works of art is becoming an increasingly popular non-destructive analytical method. The high quality XRF spectra is necessary to obtain significant information on both major and minor elements used for characterization and provenance analysis. However, there is a trade-off between the spatial resolution of an XRF scan and the Signal-to-Noise Ratio (SNR) of each pixel's spectrum, due to the limited scanning time. In this paper, we propose an XRF image super-resolution method to address this trade-off, thus obtaining a high spatial resolution XRF scan with high SNR. We use a sparse representation of each pixel using a dictionary trained from the spectrum samples of the image, while imposing a spatial smoothness constraint on the sparse coefficients. We then increase the spatial resolution of the sparse coefficient map using a conventional super-resolution method. Finally the high spatial resolution XRF image is reconstructed by the high spatial resolution sparse coefficient map and the trained spectrum dictionary.