A theoretical scheme is investigated to detect the noncommutative feature of non-Abelian geometric phases with superconducting Josephson circuits. The results show that, two degenerate dark states are generated in the considered system, and the geometric phases are naturally induced through adjusting external fluxes. By designing two composite evolutions and considering the population difference associated with the same quantum state, the noncommutative feature of the geometric phase can be shown directly. Further analyses on the feasibility and advantages indicate that the present scheme possesses the convenient operations and good quantum coherence. Thus the proposal provides an effective approach to experimentally study the noncommutative property of non-Abelian geometric phase.