High-resolution (HR) MRI is critical in assisting the doctor's diagnosis and image-guided treatment, but is hard to obtain in a clinical settings due to long acquisition time. Therefore, the research community investigated deep learning-based super-resolution (SR) technology to reconstruct HR MRI images with shortened acquisition time. However, training such neural networks usually requires paired HR and low-resolution (LR) in-vivo images, which are difficult to acquire due to patient movement during and between the image acquisition. Rigid movements of hard tissues can be corrected with image-registration, whereas the alignment of deformed soft tissues is challenging, making it impractical to train the neural network with such authentic HR and LR image pairs. Therefore, most of the previous studies proposed SR reconstruction by employing authentic HR images and synthetic LR images downsampled from the HR images, yet the difference in degradation representations between synthetic and authentic LR images suppresses the performance of SR reconstruction from authentic LR images. To mitigate the aforementioned problems, we propose a novel Unsupervised DEgradation Adaptation Network (UDEAN). Our model consists of two components: the degradation learning network and the SR reconstruction network. The degradation learning network downsamples the HR images by addressing the degradation representation of the misaligned or unpaired LR images, and the SR reconstruction network learns the mapping from the downsampled HR images to their original HR images. As a result, the SR reconstruction network can generate SR images from the LR images and achieve comparable quality to the HR images. Experimental results show that our method outperforms the state of the art models and can potentially be applied in real-world clinical settings.