A system for supporting bundled tube segments within a combustor includes an annular sleeve that extends circumferentially and axially within the combustor, a support lug that extends radially inward from the annular sleeve and an annular support frame that is disposed within the annular sleeve. The annular support frame includes an inner ring portion, an outer ring portion and a plurality of spokes that extend radially between the inner and outer ring portions. The inner ring portion, the outer ring portion and the plurality of spokes define an annular array of openings for receiving a respective bundled tube segment. The inner ring portion is connected to each bundled tube segment and the outer ring portion is coupled to the support lug.