Abstract: Considering the issue of nodes failure for energy heterogeneous wireless sensor networks, a new topology with Adjustable Degree Distribution (ADD) is constructed, and the formulas of degree distribution is obtained. And then through analyzing the effect of degree distribution characteristics on topology tolerance, the optimal topology is derived, which can assure the finish of network monitoring tasks for long under the integrated failure of nodes resulted from energy exhaust and environment damage. The simulation results show that the topology is more robustness, which provides longer lifetime.