Following the success of cloud computing, it has been shown its importance to realize various access control models in the cloud storage setting. Chinese Wall is a traditional access control model in business for solving the conflict of interest (CoI) problem, and it would be very interesting to achieve conflict-resistant in cloud storage system. However, the access control model does not ensure the privacy of users, and it may reveal the user's interest, investment tendency, etc. Therefore, it raises a big challenge to implement the Chinese Wall without compromising the user's privacy. In this paper, we focus on the Chinese Wall model and apply it to the cloud storage while protecting the access patterns of users. Specifically, we first formulate the tree-based Chinese Wall access control and then propose the Chinese Wall Protocol (called C-Wall). We prove that our C-Wall not only realizes the conflict-resistant but also protects the user's privacy with universally composable security. Besides, we also apply C-Wall to privacy-preserving cloud storage and propose the C<sup>2</sup>-Wall, which not only maintains C-Wall's features, but also ensures the sensitive files from being touched by "honest-but-curious" cloud servers. Furthermore, we evaluate our C<sup>2</sup>-Wall by theoretical analysis and experimental validation. Experimental results show its effectiveness and efficiency for practical deployment.