Cataract is one of the most common blinding eye diseases and can be treated by surgery. However, because cataract patients may also suffer from other blinding eye diseases, ophthalmologists must diagnose them before surgery. The cloudy lens of cataract patients forms a hazy degeneration in the fundus images, making it challenging to observe the patient's fundus vessels, which brings difficulties to the diagnosis process. To address this issue, this paper establishes a new cataract image restoration method named Catintell. It contains a cataract image synthesizing model, Catintell-Syn, and a restoration model, Catintell-Res. Catintell-Syn uses GAN architecture with fully unsupervised data to generate paired cataract-like images with realistic style and texture rather than the conventional Gaussian degradation algorithm. Meanwhile, Catintell-Res is an image restoration network that can improve the quality of real cataract fundus images using the knowledge learned from synthetic cataract images. Extensive experiments show that Catintell-Res outperforms other cataract image restoration methods in PSNR with 39.03 and SSIM with 0.9476. Furthermore, the universal restoration ability that Catintell-Res gained from unpaired cataract images can process cataract images from various datasets. We hope the models can help ophthalmologists identify other blinding eye diseases of cataract patients and inspire more medical image restoration methods in the future.