Task allocation is a grand challenge facing researches and practitioners in multiple unmanned aerial vehicles (multi-UAVs) missions. This paper proposes a new autonomous bio-inspired approach for efficiently allocating tasks among multiple UAVs during a mission. Task assignments are dynamically adjusted by each UAV on the basis of criteria related to the individual UAV operational status and mission parameters, without direct communication between the UAVs actively taking part in the mission. The proposed approach was inspired by the nature of locust species and their autonomous and elastic behavior in response to inside and outside impetus. Four long-standing multi-UAVs task allocation paradigms, including the auction-based, max-sum, ant colony optimization and opportunistic coordination schemes were used to benchmark the performance of the proposed approach. Experimental results demonstrated that the new approach substantially improves the net throughput and the mean task completion time while maintaining a linear running time when compared to all benchmarks under different scales of fleet size and number of tasks, demonstrating better scalability and sustainability.