<p>Existing task offloading models struggle to rapidly adapt to dynamic environmental changes in emergency scenarios, such as natural disasters or unforeseen events. To address this challenge, a meta-reinforcement learning-based task offloading method (MRLTO) for unmanned aerial vehicle (UAV)-enabled mobile edge computing (MEC) is proposed. First, an objective function for optimizing task offloading is formulated based on communication, local computing, and UAV computing models. Subsequently, the task offloading problem is reformulated as a Markov decision process (MDP). By incorporating a meta-learning framework, our approach consolidates the learning experiences of various mobile devices across diverse environments, allowing the offloading model to rapidly adapt to dynamic environmental changes. Furthermore, a dueling deep Q-network (D3QN) is employed to decouple state values and action advantage values, thereby improving task offloading decision mapping and dynamically generating more efficient offloading decisions. Finally, an experimental scenario is set up to compare MRLTO with RNOF, AGGO, and DTTO. The results show that MRLTO reduces the average latency by 8.14%, lowers the average energy consumption by 6.89%, and decreases the task drop rate by 12.89%.</p>