In order to protect the cloud resources, access control mechanisms have to be established in the cloud. However, cloud platforms have tendency to design their own security policy languages and authorization mechanisms. It leads to two issues:(i) a cloud user has to learn different policy languages to customize the permissions for each cloud, and (ii) a cloud service provider has to design and implement the authorization mechanism from the beginning, which is a high development cost. In this work, a new access control policy specification language called PML is proposed to support expressing multiple access control models like BLP, RBAC, ABAC and important features like multi-tenants. An authorization framework called PML-EM is implemented on OpenStack to centralize the authorization. PML-EM is irrelative to policy languages, access control models and programming languages that implement the authorization module. Other policies like XACML policy and OpenStack policy can be automatically translated into PML, which facilitates the migration between the clouds that both support PML-EM. The experimental results indicate PML-EM has improved the flexibility of policy management from a tenant's perspective. And the performance overhead for policy evaluation is 4.8%, and the invasiveness is about 0.42%.