Diverse styles of cytopathology images have a negative effect on the generalization ability of automated image analysis algorithms. This article proposes an unsupervised method to normalize cytopathology image styles. We design a two-stage style normalization framework with a style removal module to convert the colorful cytopathology image into a gray-scale image with a color-encoding mask and a domain adversarial style reconstruction module to map them back to a colorful image with user-selected style. Our method enforces both hue and structure consistency before and after normalization by using the color-encoding mask and per-pixel regression. Intra-domain and inter-domain adversarial learning are applied to ensure the style of normalized images consistent with the user-selected for input images of different domains. Our method shows superior results against current unsupervised color normalization methods on six cervical cell datasets from different hospitals and scanners. We further demonstrate that our normalization method greatly improves the recognition accuracy of lesion cells on unseen cytopathology images, which is meaningful for model generalization. (C) 2021 The Author(s). Published by Elsevier B.V. on behalf of Research Network of Computational and Structural Biotechnology.