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 4x to 10x super resolution. The generator of the second stage corresponds to a residual-in-residual DenseBlock and achieves 10x to 20x super resolution. The designed generator alleviates the difficulty in learning the mapping from 4x images to 20x 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.