Recently, unmanned aerial vehicle (UAV)-enabled mobile edge computing (MEC) has emerged as a practical paradigm to enable low latency computing offloading for dispersed users in the fifth generation (5G) wireless networks. However, severe security and privacy concerns are associated with the open environment between the UAVs and edge computing nodes. In this paper, we address these challenges by integrating blockchain technology into UAV-enabled MEC networks. We present an innovative Delegated Proof of Stake (DPoS) consensus mechanism where the UAV is a primary node and verification nodes are edge computing nodes selected by the reputation mechanism. To enhance mobile users’ Quality of Service (QoS), edge computing resources need to be allocated among UAV and verification nodes. Based on this, we propose the trading mechanism for resource pricing and allocation based on the two-stage Stackelberg differential game. Meanwhile, dynamic states of user demands and verification node reputations are modeled using differential equations as constraints of the objective function at various stages to simulate adaptive service requests for users and incentivize active participation for verification nodes. Simulation results prove the effectiveness of the proposed resource trading scheme and demonstrate the equilibrium and convergence status of resource pricing and allocation for edge computing.