Vehicle-mounted millimeter-wave radar is widely used in autonomous driving systems for its ability to observe road scenes at all times and in all weathers. However, the data collected by millimeter-wave radar are seriously affected by the existence of clutter. This clutter will result in false detection during object detection. To address this issue, a feature extraction network with clutter suppression is necessary. This paper proposes a new clutter suppression method for millimeter-wave Range–Angle (RA) images based on a cycle-consistency generative adversarial network (CycleGAN). The generator of the method can be used as the feature extraction network of the object detection. The method aims to convert cluttered images into clutter-free images by unsupervised learning. In this method, an attention gate (AG) is introduced into the generator, a spatial attention mechanism that improves the ability of the model to automatically learn to focus on the features of targets and suppress the clutter of the background. Additionally, the target consistency loss term is added to the loss function to maintain target integrity while suppressing network training overfitting. The public dataset CRUW is utilized to evaluate the performance of the proposed method, which is compared and analyzed with traditional methods and deep learning methods. Experimental results show that the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) of the proposed method reach 39.846 and 0.990, respectively.