Low-light image enhancement is a computer vision task that aims to improve the visual perceptual quality of images captured in poorly illuminated scenes. At present, low-light enhancement methods based on deep learning can obtain high-quality enhanced images. However, these methods fail to fully account for the statistical characteristics of different regions, with the uncertainty of images remaining poorly underutilized. Furthermore, most existing methods perform enhancement directly in the sRGB color space, where the strong coupling between color and brightness often gives rise to issues such as texture distortion, noise amplification, and color shifts. To address these issues, we propose a novel network with Uncertainty Constraint and Attention Mechanism (UCAMNet), an unsupervised framework based on the HVI color space, to improve the performance of low-light enhancement. UCAMNet first transforms the unpaired low/normal-light images from the sRGB color space to the HVI color space, which allows for a more thorough decoupling of color and brightness information, thereby decomposing the images into HV color and intensity components. Then a generative adversarial network guided by uncertainty constraint is proposed to enhance the intensity component with the guidance of variance estimation. Additionally, we further introduce a channel-spatial guided attention network to address the color distortion and noise problem, thus making the network better preserve the texture details. Extensive experimental results demonstrate that UCAMNet outperforms the state-of-the-art methods in terms of visual quality and quantitative metrics.