Most learning-based low-light image enhancement methods typically suffer from two problems. First, they require a large amount of paired data for training, which are difficult to acquire in most cases. Second, in the process of enhancement, image noise is difficult to be removed and may even be amplified. In other words, performing denoising and illumination enhancement at the same time is difficult. As an alternative to supervised learning strategies that use a large amount of paired data, as presented in previous work, this paper presents an mixed-attention guided generative adversarial network called MAGAN for low-light image enhancement in a fully unsupervised fashion. We introduce a mixed-attention module layer, which can model the relationship between each pixel and feature of the image. In this way, our network can enhance a low-light image and remove its noise simultaneously. In addition, we conduct extensive experiments on paired and no-reference datasets to show the superiority of our method in enhancing low-light images.