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A two-stage machine learning-based approach for creating synthetic phasor measurement unit (PMU) data is proposed in this article. This approach leverages generative adversarial networks (GAN) in data generation and incorporates neural ordinary differential equation (Neural ODE) to guarantee underlying physical meaning. We utilize this approach to synthetically create massive eventful PMU data, which would otherwise be difficult to obtain from the real world due to the critical energy infrastructure information (CEII) protection. To illustrate the utility of such synthetic data for subsequent data-driven methods, we specifically demonstrate the application of using synthetic PMU data for event classification by scaling up the real data set. The addition of the synthetic PMU data to a small set of real PMU data is shown to have improved the event classification accuracy by 2 to 5 percent.