With the increase of uncertain elements in power systems and extensive deployment of online monitoring devices, it is necessary to search a more real-time and robust voltage stability assessment method. This study, using PMU monitoring data, explores a novel data-driven approach for long-term voltage stability assessment based on variational autoencoder (VAE). Our method is capable of extracting the most representative features by an unsupervised data mining method in a probabilistic learning way. Different from most of familiar feature extraction methods, it regularizes latent features in an expected stochastic distribution. Furthermore, a statistical indicator by sampling latent features after variance reduction is proposed to assess long-term voltage stability. Our approach is tested in various simulated power systems with different load increment models. Other cases show the accuracy and speed of our approach for estimating voltage collapse point. These testing cases successfully demonstrate the accuracy and effectiveness of our approach.