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Transient analysis is vital to the planning and operation of electric power systems. Traditional transient analysis utilizes numerical methods to solve the differential-algebraic equations (DAEs) to compute the trajectories of quantities in the grid. For this, various numerical integration methods have been developed and used for decades. On the other hand, solving the DAEs for a relatively large system such as power grids is computationally intensive and is particularly challenging to perform online. In this paper, a novel machine learning (ML) based approach is proposed and developed to predict post-contingency trajectories of a generator in the time domain. The training data are generated by using an off-line simulation platform considering random disturbance occurrences and clearing times. As a proof-of-concept study, the proposed ML-based approach is applied to a single generator. A Long Short Term Memory (LSTM) network representation of the selected generator is successfully trained to capture the dependencies of its dynamics across a sufficiently long time span. In the online assessment stage, the LSTM network predicts the entire post-contingency transient trajectories given initial conditions of the power system triggered by system changes due to fault scenarios. Numerical experiments in the New York/New England 16-machine 86-bus power system show that the trained LSTM network accurately predicts the generator’s transient trajectories. Compared to existing numerical integration methods, the post-disturbance trajectories of generator’s dynamic states are computed much faster using the trained predictor, offering great promises for significantly accelerating both offline and online transient studies.