Time series anomaly detection is widely used in medicine, industry, finance, and transportation. However, anomaly detection faces the dual challenges of unbalanced data distribution and complex structure of time series. In recent years, GNN have attracted attention for their ability to effectively capture spatiotemporal dependencies. This paper proposes an unsupervised anomaly detection algorithm based on smoothed GNN called LSGNSF. The algorithm constructs a dynamic graph structure through LSTM and self-attention mechanism to capture the spatiotemporal dependencies of time series, and it combines Neural Spline Flow for density estimation, and uses the correlation information of time series to optimize local density estimation. Experiments show that LSGNSF improves the performance of existing algorithms by 1%–3% without the need for labeled data, providing an effective solution for anomaly detection in complex time series.