Abstract: In order to solve the Set-Union Knapsack Problem (SUKP) which is difficult to be solved by the deterministic algorithm, the quadratic greedy mutated crow search algorithm (QGMCSA) is proposed. Firstly, the greedy strategy is inproved by combining the SUKP model, and the quadratic greedy repair and optimization strategy is proposed to deal with its potential solutions. Secondly, in order to enlarge the search scope of the individual, Lévy flight is introduced into the tracking process of crow search algorithm. Finally three kinds of SUKP instances are used to verify the algorithm. Simulation results show that QGMCSA is better than binary artificial bee colony algorithm for solving SUKP, it is a an effective algorithm.