Semisupervised text classification has attracted much attention from the research community. In this paper, a novel model, the semisupervised sequential variational autoencoder (SSVAE), is proposed to tackle this problem. By treating the categorical label of unlabeled data as a discrete latent variable, the proposed model maximizes the variational evidence lower bound of the data likelihood, which implicitly derives the underlying label distribution for the unlabeled data. Analytical work indicates that the autoregressive nature of the sequential model is the crucial issue that renders the vanilla model ineffective. To remedy this, two types of decoders are investigated in the SSVAE model and verified. In addition, a reweighting approach is proposed to circumvent the credit assignment problem that occurs during the reconstruction procedure, which can further improve performance for sparse text data. Experimental results show that our method significantly improves the classification accuracy compared with other modern methods.