The most significant feature of social network sentiment data is its dynamic nature. Tackling public sentiment drift analysis, this study proposes a Gaussian mixture based hierarchical variational auto-encoder (GHVAE) model for detecting sentiment drifts. Specifically, the GHVAE applies Gaussian mixture distribution as the prior assumption of latent distribution, which corresponds to the multi-center of the latent distribution property to improve model performances. Moreover, the built-in drift measurement algorithm in the original HVAE model is revised to enlarge the distances among big drift scores and improve the classification performance. Several contrast and ablation experiments are implemented to validate the performance of the GHVAE. The results indicate the novelties of the GHVAE bring improvement in sentiment drift detection.