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Finding an accurate network null model for protein-protein interactions (PPI) networks is an important and fundamental problem in today's systems biology. A number of graph models were introduced to model and analyze PPI networks. However, because the previous network models were developed to capture specific network properties or just mimic the way that real PPI network might have evolved, the whole connectivity information of PPI networks is not utilized to learn the topological structure of the networks. In this paper we propose a novel model for PPI networks which is based on geometric random graphs and employs the entire connectivity information of PPI networks to learn its structure. The computational experiments show the superiority of the fit of our method over five other network models to PPI data. Thus, the proposed network null model could facilitate further graph-based studies of protein-protein interactions and may help infer their hidden underlying biological knowledge.