Time series anomaly detection is getting more and more attention in IT operations. Deep learning is one of the most used technologies in recent years, which realizes automatic anomaly detection on raw data. A novel algorithm combining time series decomposition and Long Short Term Memory (LSTM) is proposed in this paper. This algorithm mainly consists of four steps: 1) we use a density-based clustering algorithm to remove the sharp points in the data, and then use interpolation to complete the data; 2) we use the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm to decompose the raw data into a series of relatively simple components, called intrinsic mode functions (IMFs); 3) we use LSTM to predict the IMFs, and the sum of the results represents the predicted results of the original data; 4) we use a dynamic threshold rule and the error between the original value and the predicted value to determine whether the point is an anomaly. The experimental results on the Yahoo Webscope_S5 dataset prove the effectiveness of the proposed model.