The color variations present in histopathological images pose a significant challenge to computational pathology and, consequently, negatively affect the performance of certain pathological image analysis methods, especially those based on deep learning techniques. To date, several methods have been proposed to mitigate this issue. However, these methods either produce images with low texture retention, perform poorly when trained with small datasets, or have low generalization capabilities. In this paper, we propose a Deep Supervised Two-stage Generative Adversarial Network known as DSTGAN for stain-normalization. Specifically, we introduce deep supervision to generative adversarial networks in an innovative way to enhance the learning capacity of the model, benefiting from different model regularization methods. To make fuller use of source domain images for training the model, we drew upon semi-supervised concepts to design a novel two-stage staining strategy. Additionally, we construct a generator that can capture long-distance semantic relationships, enabling the model to retain more abundant texture information in the generated images. In the evaluation of the quality of generated images, we have achieved state-of-the-art performance on TUPAC-2016, MITOS-ATYPIA-14, ICIAR-BACH-2018 and MICCAI-16-GlaS datasets, improving the precision of classification and segmentation by 5.2% and 4.2%, respectively. Not only has our model significantly improved the quality of the stained images compared to existing stain normalization methods, but it also has a positive impact on the execution of downstream classification and segmentation tasks. Our method has further reduced the effect that staining differences have on computational pathology, thereby improving the accuracy of histopathological image analysis to some extent.