In wireless sensor networks (WSN), connected dominating set (CDS) is constructed to form the virtual backbone for hierarchical routing. Existing algorithms usually only consider how to obtain a smaller dominating sets, which ignore the instability of network itself and result to the node failure or link failure. Combining the node degrees and power factor, this paper proposes a Distributed Algorithm for Energy-Balance Minimum 2-Connected 2-Dominating Set (DA-EBM) based on the tolerance of the connected dominating set. By the simulation results of Omnet, the fault-tolerant connected dominating set constructed DA-EBM balanced energy consuming of network effectively and extend the network life cycle compared with existing algorithms.