Magnetic resonance imaging (MRI) is widely used for screening, diagnosis, image-guided therapy, and scientific research. A significant advantage of MRI over other imaging modalities such as computed tomography (CT) and nuclear imaging is that it clearly shows soft tissues in multi-contrasts. Compared with other medical image super-resolution (SR) methods that are in a single contrast, multi-contrast super-resolution studies can synergize multiple contrast images to achieve better super-resolution results. In this paper, we propose a one-level non-progressive neural network for low up-sampling multi-contrast super-resolution and a two-level progressive network for high up-sampling multi-contrast super-resolution. Multi-contrast information is combined in high-level feature space. Our experimental results demonstrate that the proposed networks can produce MRI super-resolution images with good image quality and outperform other multi-contrast super-resolution methods in terms of structural similarity and peak signal-to-noise ratio. Also, the progressive network produces a better SR image quality than the non-progressive network, even if the original low-resolution images were highly down-sampled.