Clinical diagnosis has high requirements for the resolution of medical images, but most existing medical images super- resolution (SR) methods are performed under a known or specific degradation kernel. However, the difference between the actual degradations and their assumed degradation kernels results in a severe performance drop for the advanced SR methods in real applications. This paper proposes a medical image blind super-resolution model (Med-BSR) based on an improved degradation process to handle this issue. The model makes each of the degradation factors in medical image blind SR, such as blur, noise, and downsampling, more complex and practical. Specifically, the authors use the random select/combine strategy to randomly arrange and combine the type and order of each degradation factor, which significantly expands the degradation space. The authors also improved the loss function of the primary enhanced super-resolution generative adversarial networks (ESRGAN) network. The extensive experimental results demonstrate that the authors' designed model can accurately restore the natural degradation process, which can reconstruct high-quality SR medical images. It also has a good generalization ability to realistic images simultaneously.