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 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. The proposed networks integrate multi-contrast information in a high-level feature space and optimize the imaging performance by minimizing a composite loss function, which includes mean-squared-error, adversarial loss, perceptual loss, and textural loss. Our experimental results demonstrate that 1) 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; 2) combining multi-contrast information in a high-level feature space leads to a significantly improved result than a combination in the low-level pixel space; and 3) the progressive network produces a better super-resolution image quality than the non-progressive network, even if the original low-resolution images were highly down-sampled.