Phasor Measurement Units (PMUs) have become one of the most effective tools for state awareness of complex power systems due to their synchronization, speed and accuracy. However, the complex on-site environment causes data loss, data corruption, synchronization anomaly, noise and other quality problems of the PMU data, which seriously affects various applications in the power system and even threatens the safe and stable operation of the grid. This paper proposes a PMU bad data detection method based on Long Short-Term Memory (LSTM) network. First, the advantages of LSTM in bad data detection are analyzed. Based on the characteristics of time sequence selection and memory of the LSTM network, a two-layer LSTM network architecture is constructed, and the decomposition and reconstruction method of original data is proposed. On this basis, two objective functions are defined to obtain different error characteristics. A method for determining the threshold of bad data based on decision tree is proposed, which realizes the effective detection of bad data. The feasibility and accuracy of the proposed method are verified by a large number of simulations and field data. The quality of PMU data is improved, which makes it better applied to all aspects of the power system. This work is supported by National Key Research and Development Program of China (No. 2017YFB0902900 and No. 2017YFB0902901).