Auction is widely regarded as an effective way in dynamic spectrum redistribution. Recently, considerable research efforts have been devoted to designing privacy-preserving spectrum auctions in a variety of auction settings. However, none of existing work has addressed the privacy issue in the most generic scenario, double spectrum auctions where each seller sells multiple channels and each buyer buys multiple channels. To fill this gap, in this paper we propose PP-MCSA, a Privacy Preserving mechanism for Multi-Channel double Spectrum Auctions. Technically, by leveraging garbled circuits, we manage to protect the privacy of both sellers' requests and buyers' bids in multi-channel double spectrum auctions. As far as we know, PP-MCSA is the first privacy-preserving solution for multi-channel double spectrum auctions. We further theoretically demonstrate the privacy guarantee of PP-MCSA, and extensively evaluate its performance via experiments. Experimental results show that PP-MCSA incurs only moderate communication and computation overhead.