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This study deals with the task assignment problem of heterogeneous unmanned aerial vehicle (UAV) system with the limited resources and task priority constraints. The optimization model which comprehensively considers the resource consumption, task completion effect, and workload balance is formulated. Then, a concept of fuzzy elite degree is proposed to optimize and balance the transmission of good genes and the variation strength of population during the operations of algorithm. Based on the concept, we propose the fuzzy elite strategy genetic algorithm (FESGA) to efficiently solve the complex task assignment problem. In the proposed algorithm, two unlock methods are presented to solve the deadlock problem in the random optimization process; a sudden threat countermeasure (STC) mechanism is presented to help the algorithm quickly respond to the change of task environment caused by sudden threats. The simulation results demonstrate the superiority of the proposed algorithm. Meanwhile, the effectiveness and feasibility of the algorithm in workload balance and task priority constraints are verified.