In this paper, we present a medical AttentIon Denoising Super Resolution Generative Adversarial Network (AID-SRGAN) for diographic image super-resolution. First, we present a medical practical degradation model that considers various degradation factors beyond downsampling. To the best of our knowledge, this is the first composite degradation model proposed for radiographic images. Furthermore, we propose AID-SRGAN, which can simultaneously denoise and generate high-resolution (HR) radiographs. In this model, we introduce an attention mechanism into the denoising module to make it more robust to complicated degradation. Finally, the SR module reconstructs the HR radiographs using the "clean" low-resolution (LR) radiographs. In addition, we propose a separate-joint training approach to train the model, and extensive experiments are conducted to show that the proposed method is superior to its counterparts. e.g., our proposed method achieves $31.90$ of PSNR with a scale factor of $4 \times$, which is $7.05 \%$ higher than that obtained by recent work, SPSR [16]. Our dataset and code will be made available at: https://github.com/yongsongH/AIDSRGAN-MICCAI2022.