Super-Resolution (SR) is a fundamental computer vision task, which reconstructs high-resolution images from low-resolution ones. Existing SR methods mainly recover images from clear low-resolution images, leading to unsatisfactory results when processing compressed low-resolution images. In the paper, we propose a two-stage SR method for compressed images, which consists of the Compression Artifact Removal Module (CARM) and Super-Resolution Module (SRM). The compressed low-resolution image is used to reconstruct the clear low-resolution image by CARM, and the high-resolution image is obtained by SRM. In addition, we propose a residual information distillation block to learn the texture details which are lost during the compression process. The proposed method has been validated and compared with the state of the art, and experimental results show that the proposed method outperforms other super-resolution methods in terms of visual effects and objective evaluation metrics.