Copy-move forgery can be used for hiding certain objects or duplicating meaningful objects in images. Although copy-move forgery detection has been studied extensively in recent years, it is still a challenging task to distinguish between the source and the target regions in copy-move forgery images. In this paper, a convolutional neural network-transformer based generative adversarial network (CNN-T GAN) is proposed to distinguish the source and target regions in a copy-move forged image. A generator is first utilized to generate a mask that is similar to the groundtruth mask. Then, a discriminator is trained to discriminate the true image pairs from the false ones. When the discriminator cannot discriminate the true/false image pairs accurately, the generator can be used to obtain the final localization maps of copy-move forgery. In the generator, convolutional neural network (CNN) and transformer are exploited to extract the local features and global representations in copy-move forgery images, respectively. In addition, feature coupling layers are designed to integrate the features in CNN branch and transformer branch in an interactive way. Finally, a new Pearson correlation layer is introduced to match the similarity features in source and target regions, which can improve the performance of copy-move forgery localization, especially the localization performance on source regions. To the best of our knowledge, this is the first work to utilize transformer for feature extraction in copy-move forgery localization. The proposed method can not only detect the copy-move regions, but also distinguish the source and target regions. Extensive experimental results on several commonly used copy-move datasets have shown that the proposed method outperforms the state-of-the-art methods for copy-move detection.