Since the discovery of superconductivity in twisted bilayer graphene, which initiated the field of twistronics, Moiré patterns caused by different twisting angles between stacked layers of van der Waals 2D materials show unique properties in these structures. In the present study, we examine the band structures at various rotation angles within the density functional theory framework to analyze the dependence of electronic and topological properties on the twisting angle in twisted bilayer plumbene structures. The results indicate the potential for a phase transition in the plumbene bilayer, where it can transition from a trivial insulator to a conductor. Furthermore, plumbene may exhibit characteristics of a topological insulator (TI) under specific angles. This research contains both TI and conductor structures. Our study suggests an intriguing possibility for changes in electronic and topological properties in this two-dimensional material, which can have potential applications in spintronic devices.