Infrared ship target segmentation is the important basis of infrared guided weapon in the sea-air context. Typically, accurate infrared ship target segmentation relies on a large number of pixel-level labels. However, it is difficult to obtain them. To this end, we present a method of Semi-supervised Infrared Ship Target Segmentation with Dual Branch (SeISTS-DB), which utilizes a small amount of labeled data and a large amount of unlabeled data to train model and improve segmentation performance. There are three main contributions. First, we design a target segmentation branch to generate the pseudo labels for unlabeled data. It consists of a dual learning network and a segmentation network. The dual learning network generates pseudo labels with weights for unlabeled data. The segmentation network is trained using both labeled data and unlabeled data with pseudo labels to achieve target segmentation of infrared ship, obtaining the preliminary segmentation results. Secondly, we introduce an error segmentation pixel correction branch, which contains a student network and a teacher network, to modify the pixel category error of the preliminary segmentation map. Finally, the outputs of the two branches are combined to obtain the final segmentation result. The SeISTS-DB is compared with other fully-supervised and semi-supervised methods on the infrared ship images dataset. Experimental results demonstrate that when the labeled data accounts for 1/8 of the training data, the mean Intersection over Union (mIou) is respectively improved by 15.35% and 6.19% at most. Besides, it is also compared with other methods on the public IRSTD-1k dataset, when the proportion of labeled images is 1/8, the mIoU is respectively improved by 11.76% at most compared to the state-of-the-art semi-supervised methods, demonstrating its effectiveness.