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Compressed Image Super-resolution has achieved great attention in recent years, where images are degraded with compression artifacts and low-resolution artifacts. Since the complex hybrid distortions, it is hard to restore the distorted image with the simple cooperation of super-resolution and compression artifacts removing. In this paper, we take a step forward to propose the Hierarchical Swin Transformer (HST) network to restore the low-resolution compressed image, which jointly captures the hierarchical feature representations and enhances each-scale representation with Swin transformer, respectively. Moreover, we find that the pretraining with Super-resolution (SR) task is vital in compressed image super-resolution. To explore the effects of different SR pretraining, we take the commonly-used SR tasks (e.g., bicubic and different real super-resolution simulations) as our pretraining tasks, and reveal that SR plays an irreplaceable role in the compressed image super-resolution. With the cooperation of HST and pre-training, our HST achieves the fifth place in AIM 2022 challenge on the low-quality compressed image super-resolution track, with the PSNR of 23.51dB. Extensive experiments and ablation studies have validated the effectiveness of our proposed methods. The code and models are available at https://github.com/USTC-IMCL/HST-for-Compressed-Image-SR.