Virtual backbone has been proposed recently for provisioning an efficient communication infrastructure in energy constrained wireless sensor network. In this paper, a distributed algorithm is proposed for constructing a energy-aware virtual backbone tree (EVBT) for general-purpose communication in wireless sensor network. What distinguishes our algorithm from others is that it chooses only nodes with adequate energy levels (energy level above threshold) as the member of the virtual backbone. Simulation results show that size of the EVBT is always much smaller compared to other prominent schemes. This will greatly reduce the protocol overhead. It also shows that algorithm performs competitively with others in terms total energy consumption for data delivery along the tree. The use of multiple nodes disjoint EVBTs further improves the robustness of the communication infrastructure.