Each cloud service has numerous owners and tenants, so it is necessary to construct a privacy preserving identity management and access control mechanism for cloud computing. On one hand, cloud service providers (CSP) depend on tenant's identity information to enforce appropriate access control so that cloud resources are only accessed by the authorized tenants who are willing to pay. On the other hand, tenants wish to protect their personalized service access patterns, identity privacy information and accessing newfangled cloud services by on-demand ways within the scope of their permissions. There are many identity authentication and access control schemes to address these challenges to some degree, however, there are still some limitations. In this paper, we propose a new comprehensive approach, called Privacy pReserving Identity and Access Management scheme, referred to as PRIAM, which is able to satisfy all the desirable security requirements in cloud computing. The main contributions of the proposed PRIAM scheme are threefold. First, it leverages blind signature and hash chain to protect tenant's identity privacy and implement secure mutual authentication. Second, it employs the service-level agreements to provide flexible and on-demand access control for both tenants and cloud services. Third, it makes use of the BAN logic to formally verify the correctness of the proposed protocols. As a result, our proposed PRIAM scheme is suitable to cloud computing thanks to its simplicity, correctness, low overhead, and efficiency.