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 (DNM). However, due to 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 (MOGA) to construct a Load-Balanced Virtual Backbone under PNM (LBVBP). Through simulations, we demonstrate that our proposed methods extend network lifetime by 65% on average compared with the existing state-of-the-art approaches.