In recent years, neural topic modeling has increasingly raised extensive attention due to its capacity on generating coherent topics and flexible deep neural structures. However, the widely used Dirichlet distribution in shallow topic models is difficult to reparameterize. Therefore, most existing neural topic models assume the Gaussian as the prior of topic proportions for reparameterization. Gaussian distribution does not have the sparsity like Dirichlet distribution, which limits the model’s topic extraction ability. To address this issue, we propose a novel neural topic model approximating the Dirichlet prior with the reparameterizable Kumaraswamy distribution, namely K umaraswamy N eural T opic M odel (KNTM). Specifically, we adopted the stick-breaking process for posterior inference with the Kumaraswamy distribution as the base distribution. Besides, to capture the dependencies among topics, we propose a K umaraswamy R ecurrent N eural T opic M odel (KRNTM) based on the recurrent stick-breaking construction to ensure that the model can still generate coherent topical words in high-dimensional topic space. We examined our method on five prevalent benchmark datasets over six Dirichlet-approximating neural topic models, among which KNTM has the lowest perplexity and KRNTM performance best on topic coherence and topic uniqueness. Qualitative analysis of the top topical words verifies that our proposed models can extract more semantically coherent topics compared with state-of-the-art models, further demonstrating our method’s effectiveness. This work contributes to the broader application of VAEs with Dirichlet priors.