Magnetic resonance imaging (MRI) provides images of the same anatomical structures through a multi-contrast acquisition process. Besides, since multi-contrast MRI images have similar anatomic structures, degraded images can be restored under the guidance of the reference images. However, most existing methods have the following shortages: they cannot extract long-range dependencies and non-local features, and only fuse features between degraded and reference images only in the bottleneck. Therefore, we propose a Multi-scale Style Aggregation Transformer-based network (MSAT - Net) for multi-contrast MRI restoration. MSAT-Net has a U-shaped structure comprising an encoder, a decoder, and a latent-mapping branch to prepare for style aggregation. The encoder takes the degraded and reference images as inputs, utilizing convolutional layers and crossed-dual-transformer modules to extract multi-scale features. Then, multi-scale features and latent vectors are fused by the style-aggregation module and are upsampled to generate the output images. Extensive verifications of the proposed MSAT-Net on two restoration tasks, super-resolution, and motion artifact reduction on the public IXI dataset, demonstrate that the proposed method outperforms existing methods and achieves state-of-the-art performance.