Modern power systems are incorporated with distributed energy sources to be environmental-friendly and cost-effective. However, due to system uncertainties integrated with renewable energy sources, operations require to adopt effective strategies to stabilize the entire power system. Hence, the system operator need an accurate prediction tool to forecast dynamic system states effectively. In this paper, we propose a Bayesian deep learning approach to predict the dynamic system state in a general power system. First, the input system dataset with multiple system features requires the stage of data pre-processing. Second, we obtain the dynamic state matrix of a general power system through the Newton-Raphson power flow model. Third, by incorporating the state matrix with the system features, we propose a Bayesian long short-term memory network to predict the dynamic system state variables accurately. Simulation results show that accurate prediction can be achieved at different scales of power systems through the proposed Bayesian deep learning approach.