In the cytopathology screening of cervical cancer, high-resolution digital cytopathological slides are critical for the interpretation of lesion cells. However, the acquisition of high-resolution digital slides requires high-end imaging equipment and long scanning time. In the study, we propose a GAN-based progressive multi-supervised super-resolution model called PathSRGAN (pathology super-resolution GAN) to learn the mapping of real low-resolution and high-resolution cytopathological images. With respect to the characteristics of cytopathological images, we design a new two-stage generator architecture with two supervision terms. The generator of the first stage corresponds to a densely-connected U-Net and achieves 4× to 10× super resolution. The generator of the second stage corresponds to a residual-in-residual DenseBlock and achieves 10× to 20× super resolution. The designed generator alleviates the difficulty in learning the mapping from 4× images to 20× images caused by the great numerical aperture difference and generates high quality high-resolution images. We conduct a series of comparison experiments and demonstrate the superiority of PathSRGAN to mainstream CNN-based and GAN-based super-resolution methods in cytopathological images. Simultaneously, the reconstructed high-resolution images by PathSRGAN improve the accuracy of computer-aided diagnosis tasks effectively. It is anticipated that the study will help increase the penetration rate of cytopathology screening in remote and impoverished areas that lack high-end imaging equipment.