Cardiac image segmentation is crucial for the assessment of heart anatomy and function. Deep learning (DL) has been widely employed for cardiac image segmentation and the accuracy of the segmentation has improved due to the advances in DL research and the existence of large cardiac datasets. In this study, we introduce a DL framework based on adversarial training for the delineation of the left ventricle (LV) from cardiac magnetic resonance imagining (CMRI). Our framework consists of two networks: the segmenter which is a neural network that predicts segmentation maps for the myocardium, the discriminator which is a convolutional neural network that discriminates between the ground truth and the predicted segmentation maps. We investigate two different architectures for the segmenter (Unet and TransUnet). The adversarial training can identify and correct the differences between the predicted and the ground truth maps and results in better segmentation accuracy than stand-alone Unet or TransUnet. The proposed framework has been evaluated on cine CMRI, collected from 100 patients, and evaluated using different metrics (Dice coefficient, Jaccard Index, and Hausdorff distance). The results documented an improvement of the segmentation accuracy (0.91, 0.82, 4.69 mm) using the proposed framework with TransUnet compared to the segmentation obtained by stand-alone Unet (0.75, 0.68, 7.54 mm).