In this paper, we propose an adversarial learning network for the task of multi-style image captioning (MSCap) with a standard factual image caption dataset and a multi-stylized language corpus without paired images. How to learn a single model for multi-stylized image captioning with unpaired data is a challenging and necessary task, whereas rarely studied in previous works. The proposed framework mainly includes four contributive modules following a typical image encoder. First, a style dependent caption generator to output a sentence conditioned on an encoded image and a specified style. Second, a caption discriminator is presented to distinguish the input sentence to be real or not. The discriminator and the generator are trained in an adversarial manner to enable more natural and human-like captions. Third, a style classifier is employed to discriminate the specific style of the input sentence. Besides, a back-translation module is designed to enforce the generated stylized captions are visually grounded, with the intuition of the cycle consistency for factual caption and stylized caption. We enable an end-to-end optimization of the whole model with differentiable softmax approximation. At last, we conduct comprehensive experiments using a combined dataset containing four caption styles to demonstrate the outstanding performance of our proposed method.