In this study, we propose and experimentally demonstrate a novel kind of Tamm plasmon topological superlattice (TTS) by engineering Tamm photonic crystals (TPCs) belonging to a different class of topology. Utilizing specifically designed double-layer metasurfaces etching on planar multilayered photonic structures, the TPC that supports the Tamm plasmon photonic bandgap is realized in the visible regime. Through the coupling of topological interface states existing between different TPCs, hybrid topological interface states of Tamm plasmon, called supermodes, are obtained that can be fully described by a tight-binding model. Meanwhile, we can achieve a tunable bandwidth of supermodes via varying the etching depth difference between double-layer metasurfaces. We show that the bandwidth decreases with the increase of etching depth difference, resulting in a nearly flat dispersion of supermodes with strong localization regardless of excitation angles. All the results are experimentally verified by measuring angular-resolved reflectance spectra. The TTS and supermodes proposed here open a new pathway for the manipulation of Tamm plasmons, based on which various promising applications such as integrated photonic devices, optical sensing, and enhancing light-matter interactions can be realized.