The non-uniform illumination or imbalanced intensity in medical images brings challenges for automated screening, examination and diagnosis of diseases. Previously, CycleGAN was proposed to transform input images into enhanced ones without paired images. However, it did not consider many local details of the structures, which are essential for medical images. In this paper, we propose a Cycle Structure and Illumination constrained GAN (CSI-GAN), for medical image enhancement. Inspired by CycleGAN based on the global constraints of the adversarial loss and cycle consistency, the proposed CSI-GAN treats low and high quality images as those in two domains and computes local structure and illumination constraints for learning both overall characteristics and local details. To evaluate the effectiveness of CSI-GAN, we have conducted experiments over two medical image datasets: corneal confocal microscopy (CCM) and endoscopic images. The experimental results show that our method yields better performance than both conventional methods and other deep learning based methods. As a complementary output, we will release the CCM dataset to the public in the future.