Mobile edge computing (MEC) has emerged as one of the key technical aspects of the fifth-generation (5G) networks. The integration of MEC with resource-constrained unmanned aerial vehicles (UAVs) greatly enables flexible resource provisioning for supporting dynamic and computation-intensive UAV applications. Existing resource trading could facilitate this paradigm with proper incentives, which, however, may often incur unexpected negotiation latency and energy consumption, trading failures and unfair pricing, due to the unpredictable nature of the resource trading process. Motivated by these challenges, an efficient futures-enabled resource trading mechanism for edge computing-assisted UAV network is proposed, where a mutually beneficial and risk-tolerable forward contract is devised to promote resource trading between an MEC server (seller) and a UAV (buyer) with multiple tasks. Two key problems i.e. futures contract design before trading, and transmission power optimization during trading are studied. By analyzing historical statistics associated with future resource supply, demand, and air-to-ground communication quality, the contract design is formulated as a multi-objective optimization problem aiming to maximize both the seller’s and the buyer’s expected utilities, while estimating their acceptable risk tolerance. Accordingly, we propose an efficient bilateral negotiation scheme to help players reach a trading consensus on the amount of resources and the relevant price. For the power optimization problem, we develop a practical algorithm that enables the buyer to determine its optimal transmission power via convex optimization techniques. Comprehensive simulations demonstrate that the proposed mechanism offers mutually beneficial utilities to players, while achieving commendable performance on trading failures and fairness, negotiation latency and cost, comparing with baseline methods.