UAV flight data is an important state parameter reflecting its own flight safety, and it is a key initiative to improve the overall flight safety of UAVs through abnormal detection of flight data. Although data-driven methods do not require expert a priori knowledge and accurate physical models, the lack of parameter selection and a single model for the detection network structure make the detection model overfitting due to too many parameters and failing to effectively capture data anomaly patterns. In this paper, a VAE-LSTM based UAV flight data anomaly detection modeling method is proposed by combining the advantages of Variational Auto-Encoders and Long Short-Term Memory networks. First, the Kendall correlation analysis method is introduced for selecting relevant dependent flight data parameter sets; Second, the parameter sets with correlation are trained on the designed VAE-LSTM deep hybrid model to learn the relational mapping between different data features; And lastly, the validation is performed with unsupervised anomaly detection in real multi-dimensional Unmanned Aerial Vehicle flight data. The experimental results show that the various average performance metrics of precision, detection rate, accuracy, F1 score and false detection rate of VAE-LSTM reach 95.24%, 98.71%, 98.8%, 96.82%, and 1.31%, respectively, and show overall better anomaly detection performance compared to KNN, OC-SVM, VAE, and LSTM models.