Real-time Transient Stability Assessment (TSA) is essential for prompt control decisions that lead to a stable power system. With the wide deployment of Phasor Measurement Units (PMUs) in power grids, data-driven TSA approaches, particularly those based on machine learning (ML) techniques, have become increasingly relevant in recent years. Within cycles, the well-trained ML-based TSA classifiers enable accurately assessing the post-fault transient stability of a power system. However, events that lead to transient instability are rare. Hence, the training datasets used by ML-based classifiers are highly imbalanced, challenging the accuracy of these methods. An imbalanced dataset, where the number of unstable samples is significantly lower than the number of stable samples, will result in an inaccurate and biased classifier. To address the problem of imbalanced data, the Generative Adversarial Network (GAN) is utilized to generate synthetic unstable datasets by learning from the real unstable transient data, with a goal to balance the distribution of the stable and unstable datasets. To learn the spatial and temporal correlations of the PMU data, a Recurrent Neural Network (RNN) and the correlation loss are utilized to construct the GAN model. Comparison with other data resampling methods demonstrates that the developed GAN model addresses the problem of an imbalanced training dataset, and results in more accurate machine learning-based algorithms for TSA.