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Deep learning is a popular machine learning approach which has achieved a lot of progress in all traditional machine learning areas. Internet of thing (IoT) and Smart City deployments are generating large amounts of time-series sensor data in need of analysis. Applying deep learning to these domains has been an important topic of research. The Long-Short Term Memory (LSTM) network has been proven to be well suited for dealing with and predicting important events with long intervals and delays in the time series. LTSM networks have the ability to maintain long-term memory. In an LTSM network, a stacked LSTM hidden layer also makes it possible to learn a high level temporal feature without the need of any fine tuning and preprocessing which would be required by other techniques. In this paper, we construct a long-short term memory (LSTM) recurrent neural network structure, use the normal time series training set to build the prediction model. And then we use the predicted error from the prediction model to construct a Gaussian naive Bayes model to detect whether the original sample is abnormal. This method is called LSTM-Gauss-NBayes for short. We use three real-world data sets, each of which involve long-term time-dependence or short-term time-dependence, even very weak time dependence. The experimental results show that LSTM-Gauss-NBayes is an effective and robust model.