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Face restoration is important in face image processing, and has been widely studied in recent years. However, previous works often fail to generate plausible high quality (HQ) results for real-world low quality (LQ) face images. In this paper, we propose a new progressive semantic-aware style transformation framework, named PSFR-GAN, for face restoration. Specifically, instead of using an encoder-decoder framework as previous methods, we formulate the restoration of LQ face images as a multi-scale progressive restoration procedure through semantic-aware style transformation. Given a pair of LQ face image and its corresponding parsing map, we first generate a multi-scale pyramid of the inputs, and then progressively modulate different scale features from coarse-to-fine in a semantic-aware style transfer way. Compared with previous networks, the proposed PSFR-GAN makes full use of the semantic (parsing maps) and pixel (LQ images) space information from different scales of input pairs. In addition, we further introduce a semantic aware style loss which calculates the feature style loss for each semantic region individually to improve the details of face textures. Finally, we pretrain a face parsing network which can generate decent parsing maps from real-world LQ face images. Experiment results show that our model trained with synthetic data can not only produce more realistic high-resolution results for synthetic LQ inputs and but also generalize better to natural LQ face images compared with state-of-the-art methods. Codes are available at https://github.com/chaofengc/PSFRGAN.