Unmanned aerial vehicle (UAV) assisted mobile edge computing (MEC) systems have emerged as a promising technology with the capability to expand terrestrial networks. UAVs, working as edge computing nodes and mobile base stations, can be deployed closer to user equipment (UEs). However, with the rapid increase of UEs, the scarcity of spectrum resources and computing resources has become a critical challenge for future mobile communication systems. Additionally, the inherent characteristics of wireless transmission and untrusted broadcasting pose significant security and privacy concerns for multi-UAV networks. To address these issues, this paper presents a blockchain-based resource trading mechanism (BRTM) and a double auction-based resource trading algorithm (DARA) for multi-UAV edge computing systems. It combines blockchain technology with double auction theory to ensure the security and fairness of resource trading. The relations between UEs and UAVs as a two-stage Stackelberg game is formulated and a pricing-based incentive strategy is proposed. The proposed scheme encourages active participation from both UEs and UAVs while maximizing the sum of their utilities. The security assessment and numerical outcomes show that the proposed method is effective and outperforms other benchmark schemes.