Data resources in open computing environments (including big data, internet of things and cloud computing) are characterized by large scale, wide source, and strong dynamics. Therefore, the user-permission relationship of open computing environments has a huge scale and will be dynamically adjusted over time, which enables effective permission management in the role based access control (RBAC) model to become a challenging problem. In this paper, we design an evolution mechanism of access control roles for open computing environments. The mechanism utilizes the existing user-permission relationship in the current system to mine the access control role and generate the user-role and role-permission relationship. When the user-permission relationship changes, the roles are constantly tuned and evolved to provide role support for access control of open computing environments. We propose a novel genetic-based role evolution algorithm that can effectively mine and optimize roles while preserving the core permissions of the system. In addition, a role relationship aggregation algorithm is proposed to realize the clustering of roles, which provides a supplementary reference for the security administrator to give the role real semantic information. Experimental evaluations in real-world data sets show that the proposed mechanism is effective and reliable.