In the new era characterized by the modernization of national governance, fair competition is the inherent requirement of building a modern market system. However, the abuse of administrative power by administrative organs to excessively interfere in free-market competition is widespread, seriously damaging the market competition order in China. To avoid the unreasonable intervention of administrative organs in the market economy, restrain the administrative acts of administrative organs, and form a highly “competitive” market environment, the fair competition review system came into being. With the rapid development of blockchain technology, new ideas are provided for the research of fair-trade protocols. Aiming at the system performance bottleneck and high-cost problems caused by centralized processing in traditional fair transaction schemes based on trusted third parties, a fair transaction scheme based on fuzzy signature is proposed. In the proposed scheme, the signature model uses concurrent signature, and both parties hold their own key numbers, which are released through blockchain transactions to bind their signatures. In the whole process, both parties can complete the contract signing without the assistance of a centralized third party. Based on analyzing the security of the proposed scheme, the performance of the proposed scheme is further compared with other similar schemes of the same kind, which shows that the proposed scheme has higher computational efficiency.