In this paper, a data-driven online approach is established to detect events in power systems in real time. The approach does not require prior knowledge of the power system model or its parameters. Instead, it utilizes a long short-term memory (LSTM) model to capture the state evolution of the power system. Due to the expressiveness of the LSTM model, it is able to track the system states with small prediction error when it operates under normal conditions. However, when the system is perturbed by certain events that cannot be predicted by the model, the prediction error will increase dramatically. Thus, by tracking the prediction error of the trained LSTM model, the data-driven online approach is able to detect events in a timely fashion. The event detection problem is then cast into the quick change detection framework, where a Cumulative Sum (CUSUM) based approach is proposed. To overcome the difficulty that the statistics of the prediction error when events happen is generally unknown beforehand, a generalized likelihood ratio test (GLRT) is incorporated into the CUSUM procedure. A Rao-test is then adopted to reduce the computationally complexity of GLRT. Finally, the LSTM based event detection approach is validated with real-world PMU measurements.