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Convolutional neural network (CNN), in particular the Unet, is a powerful method for medical image segmentation. To date Unet has demonstrated state-of-art performance in many complex medical image segmentation tasks, especially under the condition when the training and testing data share the same distribution (i.e. come from the same source domain). However, in clinical practice, medical images are acquired from different vendors and centers. The performance of a U-Net trained from a particular source domain, when transferred to a different target domain (e.g. different vendor, acquisition parameter), can drop unexpectedly. Collecting a large amount of annotation from each new domain to retrain the U-Net is expensive, tedious, and practically impossible. In this work, we proposed a generic framework to address this problem, consisting of (1) an unpaired generative adversarial network (GAN) for vendor-adaptation, and (2) a Unet for object segmentation. In the proposed Unet-GAN architecture, GAN learns from Unet at the feature level that is segmentation-specific. We used cardiac cine MRI as the example, with three major vendors (Philips, Siemens, and GE) as three domains, while the methodology can be extended to medical images segmentation in general. The proposed method showed significant improvement of the segmentation results across vendors. The proposed Unet-GAN provides an annotation-free solution to the cross-vendor medical image segmentation problem, potentially extending a trained deep learning model to multi-center and multi-vendor use in real clinical scenario.