In this paper, we address the issue of data trading in big data markets. Data trading problems have attracted increased attention recently, as the economic benefits and potential of big data trading are substantial and varied. However, how to effectively trade data between the data owners (sellers) and data collectors/users (buyers) is far from settled, and requires careful design. Auction mechanisms have been applied across many fields, and have significant potential to facilitate data transactions in a fair, truthful, and secure way. Nonetheless, a truthful auction must ensure the property of incentive compatibility, meaning that the bidders can obtain highest utility if and only if they submit their bids and asks truthfully. Furthermore, a truthful and fair auction should also protect the optimal auction results from being manipulated by false-name bidding attacks, where users (participants) utilize multiple identities or accounts to influence the auction results. To tackle these issues, we propose a Multi-round False-name Proof Auction (MFPA) scheme, which enables data trading among data owners (sellers) and data collectors (buyers). We prove that our MFPA scheme achieves the properties of incentive compatibility, false-name bidding proofness, and computational efficiency. The experimental results demonstrate that MFPA achieves good performance in terms of social surplus, satisfaction ratio, and computation overhead.