Image style transfer is a crucial task in computer vision, aiming to apply a specific artistic style to a content image. In recent years, transformer-based methods have made remarkable progress in this field, demonstrating outstanding performance in generating high-quality stylized images. However, these methods still face challenges in computational efficiency and fine-grained detail control. Moreover, most existing style transfer approaches rely on paired training data, which is often unavailable in real-world scenarios. To address these issues, this paper proposes an unpaired image style transfer algorithm that combines the Mamba model with Generative Adversarial Networks (GANs). By introducing Mamba-GAN, the proposed method enhances computational efficiency and eliminates the dependency on paired training samples. Furthermore, a novel scanning strategy is incorporated into the Mamba-GAN network input to improve the control of stylization details. Experimental results on the Cycle-GAN image translation dataset demonstrate that the proposed method achieves efficient and visually impressive style transfer results.