In this paper, we investigate the construction of rings overlay in wireless sensor networks for enhancing the robustness of sensor data collection. Rings overlay is a class of multi-path routing structure that exploits the broadcast nature of wireless communication to cope with communication failures. We propose a distributed approach for constructing the rings overlay to allow sensor nodes to benefit from multi-path routing as much as possible. The proposed approach does not require sensor nodes to have global knowledge about the entire network. Experimental results show that the proposed construction approach significantly improves the robustness of sensor data collection through the rings overlay compared with a baseline greedy construction approach.