In view of the problem that the IP address jump law is easy to predict in the current mobile target defense, this paper proposes a network address jump active defense method based on a dynamic random graph, designed to improve the unpredictability of IP address translation. Firstly, in order to make IP address transformation unpredictable in space and time, a random graph model is designed to generate a pseudo-random sequence of IP address randomization; these pseudo-random can meet the unpredictability of IP address translation in both space and time. Then, based on these pseudo-random sequences and IP address pool, a random map generation algorithm is proposed, which generates highly random IP address sequences through chaotic mapping (Logistic mapping) combined with encryption perturbation technology, meeting the requirements of resisting analysis attacks, while these transformed IP addresses are adapted to network target defense. And finally, this article uses buildMininet to build a cloud network trusted environment, by testing the spatial randomization and temporal randomization of the Random mapping model (CRM), the results show that the CRM model has a good effect on improving the local randomness. The test results of the ablation experiment further show that the CRM model can improve the local randomness while maintaining the global randomness.