In the traditional cloud storage auditing, users individually audit the cloud storage provider (CSP). However, users may pay the redundant auditing cost when they have similar auditing results. For example, a lot of users may get fail results when the CSP's service occurs accidents. In the worst case, the overall auditing cost linearly increases with the number of users. We propose a cooperative auditing model to let user share their auditing results in a friendship-based social network so that their overall auditing cost can be reduced. Furthermore, we design an auditing coalition game based on cooperative game theory, where not only users’ individual interest but their entire benefit is c onsidered. We present two algorithms to find out an optimal way of forming auditing c oalitions. The first algorithm determines an optimal coalition in one iteration. In the second algorithm, after iteratively adjusting users’ trust relationships, users may change to join another coalition if they receive wrong auditing results. The results of the one-iteration experiment show that the more number of users, the more auditing cost reduction. Specifically, the auditing cost can be reduced by 96% with respect to the original non-cooperative auditing model. In the multi-iteration experiment, the accuracy of users’ auditing results can be improved from 88% to 100%.