Most existing algorithms used for constructing virtual backbones are based on the ideal deterministic network model (DNM) in which any pair of nodes is either fully connected or completely disconnected. Different from DNM, the probabilistic network model (PNM), which presumes that there is a probability to connect and communicate between any pair of nodes, is more suitable to the practice in many real applications. In this paper, we propose a new algorithm to construct reliable virtual backbone in probabilistic wireless sensor networks. In the algorithm, we firstly introduce Effective Degree of Delivery Probability (EDDP) to indicate the reliable degree of nodes to transfer data successfully, and then exclude those nodes with zero EDDP from the candidate dominator set to construct a reliable connected dominating set (CDS). Moreover, each dominatee selects the neighbor dominator with the maximum delivery probability to transfer data. Through simulations, we demonstrate that our proposed algorithm can remarkably prolong the network lifetime compared with existing typical algorithms.