The deep learning algorithms achieved promising results in the computational pathology in recent decade but the high data demand of the deep learning algorithms get stuck in the multi-institutional data collaborations. The federated learning is a novel concept, which proposes to train the models of the different sites collaboratively via an orchestrating server without leaking private data. However, the imbalanced data distributions are challenging for federated learning and result in performance decrease and destabilization. In this study, the federated version of the neural style transfer algorithm, which was offered by Gatys et al. is proposed as a data augmentation method on the highly class imbalanced configuration of Chaoyang colorectal cancer imaging dataset. The proposed method works by firstly selecting characteristic style images and then generating the gram style matrices on the local sites and then transferring them to the other imbalanced sites by not leaking any private data. The proposed method contributed the ACC, F1 Score and AUC results of pure FL by 22.07%, 42.51% and 9.65% using only 20 images for content and 5 images for style. Additionally, the experiments having different content and style numbers achieved the satisfactory and consisting results.