Non-Abelian topological theory enables the classification of multigap systems and captures complex structures beyond conventional band topology. In this study, we propose a four-band non-Abelian topological insulator model in the one-dimensional ladder lattice. This model features a pair of flat bands and supports diverse edge states tunable via system parameters. More importantly, the realization in such low-complexity systems enlarges the application potential of the non-Abelian topological theory. To demonstrate this, we design a topolectrical circuit simulation scheme, laying a direct theoretical foundation for the experimental verification of non-Abelian topological insulators. Both the theoretical analysis and the simulation scheme show that the flat-band system establishes a practical, accessible platform that directly facilitates the realization and future application of non-Abelian topological phases.

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• Flat bands
• Symmetry protected topological states
• Topolectrical circuits
• Topological phase transition
• Topological insulators
• Discrete symmetries in condensed matter
• Non-Abelian models
• Tight-binding model