Since there is no infrastructure in wireless sensor networks, the CDS (Connected Dominating Set) has been widely used as a virtual backbone. It is desirable that the virtual backbone is fault tolerate because node and link failure are inherent in wireless sensor networks. In this paper, we propose an algorithm which constructs a MESH-CDS in a localized manner in order to resist the failure of one node on the backbone. The size of the MESH-CDS is within a constant factor of optimal CDS for the sake of saving energy. Simulation results show that it can improve the energy efficiency of networks.