In multi-hop wireless networks, the use of virtual backbone can greatly simplify routing, broadcasting, as well as energy/bandwidth saving. However, constructing a virtual backbone is costly and time-consuming because of the inevitable transmission interference during the process of the construction. In the literature, most of virtual backbone construction algorithms did not take the interference issue into consideration. To the best of our knowledge, our proposed algorithm is the first fully-distributed, interference-aware virtual backbone construction algorithm that has a proven bound on the construction latency. Besides, our proposed algorithm can be applied to the leader election problem, and such application results in a fully-distributed and interference-aware leader election algorithm of time complexity O(n log n) (where n is the number of nodes). This new leader election algorithm is practical in wireless networks because interference has already been dealt with; is also results in the fastest interference-aware leader election algorithm to the best of our knowledge.