When modeling the behavior of the Internet, it is vital to obtain a good description of its topology because structure fundamentally affects function. Here we introduce the Positive-Feedback Preference (PFP) model, which is the most precise and complete Internet topology generator to date. The model uses two generic mechanisms based on observations on Internet history data, namely the Interactive Growth of new nodes and new internal links, combined with a novel nonlinear preferential probability, which is described by a positive-feedback mechanism. The PFP model accurately reproduces many topological properties of the AS-level Internet, including degree distribution, the maximum degree, rich-club connectivity, disassortative mixing, shortest-path length, short cycles and betweenness centrality. These properties are relevant to crucial network behaviors, such as routing efficiency, flexibility and traffic distribution. The PFP model can be used in more representative Internet simulations. © 2005 IEEE.