It is a common practice to simulate some historical or test systems to validate the ef?ciency of new methods or concepts. However, there are only a small number of existing power system test cases, and validation and evaluation results, obtained using such a limited number of test cases, may not be deemed suf?cient or convincing. In order to provide more available test cases, a new random graph generation algorithm, named ‘‘dualstage constructed random graph’’ algorithm, is proposed to effectively model the power grid topology. The algorithm generates a spanning tree to guarantee the connectivity of random graphs and is capable of controlling the number of lines precisely. No matter how much the average degree is, whether sparse or not, random graphs can be quickly formed to satisfy the requirements. An approach is developed to generate random graphs with prescribed numbers of connected components, in order to simulate the power grid topology under fault conditions. Our experimental study on several realistic power grid topologies proves that the proposed algorithm can quickly generate a large number of random graphs with the topology characteristics of real-world power grid.