Anomaly detection is crucial to the safety of complex electromechanical equipment. With the rapid accumulation of industrial data, intelligent methods without human intervention have become the mainstream of anomaly detection. Among them, variational autoencoder (VAE) performs well in anomaly detection with missing fault samples due to the self-supervised learning paradigm. However, the data from electromechanical equipment is usually non-Gaussian, making it difficult for the standard VAE based on Gaussian distribution to recognize the abnormal states. To solve the above problems, we proposed multi-mode non-Gaussian VAE (MNVAE) to detect anomalies from unknown distribution vibration signals without fault samples or prior knowledge. Firstly, the encoder maps the input to a Gaussian mixture distribution in latent space and samples a latent variable from it, after which the Householder Flow is applied to the latent variable to capture more abundant features. Finally, to describe the non-Gaussianity of the signal, Weibull distribution serves as the likelihood function of the reconstructed signal output from the decoder and as the basis for anomaly discrimination. In comparison to 6 related methods, our method yields the best results across various datasets. Through further experiments, the robustness of our method is proved and the proposed improvements are effective.