A connected dominating set (CDS) is used as a virtual backbone (VB) for efficient routing and broadcasting in wireless sensor networks (WSNs). Currently, almost all existing works focus on constructing minimum-sized CDS under the deterministic network model. However, because of the existence of many probabilistic lossy links in WSNs, it is more practical to obtain a VB under the realistic probabilistic network model (PNM). Moreover, load-balance factor cannot be neglected when constructing a VB to prolong network lifetime. Hence, in this paper, we propose a multi-objective genetic algorithm to construct a load-balanced VB under PNM. Through simulations, we demonstrate that our proposed methods extend network lifetime by 69% on average compared with the existing state-of-the-art approaches.