In this paper, we propose a new notion called k-times attribute-based anonymous access control, which is particularly designed for supporting cloud computing environment. In this new notion, a user can authenticate himself/herself to the cloud computing server anonymously. The server only knows the user acquires some required attributes, yet it does not know the identity of this user. In addition, we provide a k-times limit for anonymous access control. That is, the server may limit a particular set of users (i.e., those users with the same set of attribute) to access the system for a maximum k-times within a period or an event. Further additional access will be denied. We also prove the security of our instantiation. Our implementation result shows that our scheme is practical.