Time series anomaly detection is widely used to monitor the equipment sates through the data collected in the form of time series. At present, the deep learning method based on generative adversarial networks (GAN) has emerged for time series anomaly detection. However, this method needs to find the best mapping from real-time space to the latent space at the anomaly detection stage, which brings new errors and takes a long time. In this paper, we propose a long short-term memory-based variational autoencoder generation adversarial networks (LSTM-based VAE-GAN) method for time series anomaly detection, which effectively solves the above problems. Our method jointly trains the encoder, the generator and the discriminator to take advantage of the mapping ability of the encoder and the discrimination ability of the discriminator simultaneously. The long short-term memory (LSTM) networks are used as the encoder, the generator and the discriminator. At the anomaly detection stage, anomalies are detected based on reconstruction difference and discrimination results. Experimental results show that the proposed method can quickly and accurately detect anomalies.