Protein-protein interaction (PPI) networks provide insights into understanding of biological processes, function and the underlying complex evolutionary mechanisms of the cell. Modeling PPI network is an important and fundamental problem in system biology, where it is still of major concern to find a better fitting model that requires less structural assumptions and is more robust against the large fraction of noisy PPIs. In this paper, we propose a new approach called t-logistic semantic embedding (t-LSE) to model PPI networks. t-LSE tries to adaptively learn a metric embedding under the simple geometric assumption of PPI networks, and a non-convex cost function was adopted to deal with the noise in PPI networks. The experimental results show the superiority of the fit of t-LSE over other network models to PPI data. Furthermore, the robust loss function adopted here leads to big improvements for dealing with the noise in PPI network. The proposed model could thus facilitate further graph-based studies of PPIs and may help infer the hidden underlying biological knowledge. The Matlab code implementing the proposed method is freely available from the web site: http://home.ustc.edu.cn/~yzh33108/PPIModel.htm.