Synthetic aperture radar (SAR) imaging has round-the-clock data acquisition capability regardless of light and climate constraints, so it has been widely used for ship detection. However, SAR images usually suffer lower imaging quality, which may result in indistinct contours and non-negligible noise. Therefore, the manual labeling for SAR images is expensive, leading to a lack of training data in the task of ship detection. In this article, we propose a route by utilizing domain adaptive methods to transfer information from labeled visible images (source domain) to unlabeled SAR images (target domain) for ship detection. To address the distribution mismatch between domains, we develop a novel imbalanced discriminant alignment (IDA) approach to improve the discriminant ability of the network and prevent negative migration. The core of the IDA approach is applying a new loss function called imbalanced prediction consistency (IPC) loss to describe the domain classifier consistency, and we further provide theoretical analysis for the effectiveness of the IPC loss. IDA ensures consistency at the image level and instance level, and focuses on the consistency of the source domain to enhance the feature extraction capability of the adversarial network. The theoretical discussion has proven that a necessary and sufficient condition for convergence of the IPC loss is that the two discriminant probabilities converge to 0 at the discriminant distance we define. Experimental results have indicated the advantage of IDA when compared with other domain adaptation SAR ship detection methods.