As well-known, inner functions play an important role in the study of bounded analytic function theory. In recent years, persistence module theory, as a main tool applied to Topological Data Analysis, has received widespread attention. In this talk, we introduce the persistence modules arised from the level sets of inner functions. Some properties of these persistence modules are shown. Furthermore, we demonstrate that the interleaving distance of the persistence modules is continuous with respect to the supremum norm for a class of Blaschke products, which could be used to discuss the path-connectedness of Blaschke products. This work is joint with Jiaxing He, Xiao Wang and Yue Xin.