Neural topic models have been widely used in discovering the latent semantics from a corpus. Recently, there are several researches on hierarchical neural topic models since the relationships among topics are valuable for data analysis and exploration. However, the existing hierarchical neural topic models are limited to generate a single topic tree. In this study, we present a nonparametric forest-structured neural topic model by firstly applying the self-attention mechanism to capture parent-child topic relationships, and then build a sparse directed acyclic graph to form a topic forest. Experiments indicate that our model can automatically learn a forest-structured topic hierarchy with indefinite numbers of trees and leaves, and significantly outperforms the baseline models on topic hierarchical rationality and affinity.