An important issue on the formation of concentric eyewalls in a tropical cyclone is the development of the symmetric structure from the asymmetric convection. We propose with a nondivergent barotropic model that the concentric vorticity structure formation is a result of vortex interaction between a small and strong inner vortex (the tropical cyclone core) and the neighboring weak vortices (the vorticity induced by the moist convection outside the central vortex of a tropical cyclone). The results highlight the pivotal role of the strength (in terms of vorticity) of the inner core vortex in maintaining itself, and in stretching, organizing and stabilizing the outer vorticity field. Specifically, the core vortex induces a differential rotation across the large and weak vortex to strain out the latter into a vorticity band surrounding the former. The contraction of the secondary tangential wind maximum is a salient feature of the straining out of a large, weak vortex into a concentric vorticity band. The outer band is stabilized by the Fjortoft sufficient condition for stability because the strong inner vortex can cause the wind at the inner edge to be stronger than the outer edge, allowing the vorticity band and therefore the concentric structure to be sustained. Moreover, the inner vortex has to be strong in vorticity not only to maintain itself against any deformation field from the outer vortices but also to maintain a smaller enstrophy cascade and to resist the merger process into a monopole. The negative vorticity anomaly in the moat serves as a ``shield" or a barrier to the further inward mixing the outer vorticity field. In general, the formation of a concentric vorticity structure requires a very strong core vortex (core at least 6 times stronger in vorticity strength than the neighboring vortices), a relatively larger area of the neighboring vorticity field (larger in size than the core vortex), and a separation distance not too far away from the core vortex (3 to 4 times the core vortex radius).