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The problem of dynamic spectrum redistribution has been extensively studied in recent years. Auction is believed to be one of the most effective tools to solve this problem. A great number of strategy-proof auction mechanisms have been proposed to improve spectrum allocation efficiency by stimulating bidders to truthfully reveal their valuations of spectrum, which are the private information of bidders. However, none of these approaches protects bidders' privacy. In this paper, we present SPRING, which is the first Strategy-proof and PRivacy preservING spectrum auction mechanism. We not only rigorously prove the properties of SPRING, but also extensively evaluate its performance. Our evaluation results show that SPRING achieves good spectrum redistribution efficiency with low overhead.