Topic modeling has emerged as a valuable tool for discovering patterns and topics within large collections of documents. However, when cross-analysis involves multiple parties, data privacy becomes a critical concern. Federated topic modeling has been developed to address this issue, allowing multiple parties to jointly train models while protecting pri-vacy. However, there are communication and performance challenges in the federated sce-nario. In order to solve the above problems, this paper proposes a method to establish a federated topic model while ensuring the privacy of each node, and use neural network model pruning to accelerate the model, where the client periodically sends the model neu-ron cumulative gradients and model weights to the server, and the server prunes the model. To address different requirements, two different methods are proposed to determine the model pruning rate. The first method involves slow pruning throughout the entire model training process, which has limited acceleration effect on the model training process, but can ensure that the pruned model achieves higher accuracy. This can significantly reduce the model inference time during the inference process. The second strategy is to quickly reach the target pruning rate in the early stage of model training in order to accelerate the model training speed, and then continue to train the model with a smaller model size after reaching the target pruning rate. This approach may lose more useful information but can complete the model training faster. Experimental results show that the federated topic model pruning based on the variational autoencoder proposed in this paper can greatly accelerate the model training speed while ensuring the model's performance.