In order to solve discrete multi-objective optimization problems, a non-dominated sorting quantum particle swarm optimization (NSQPSO) based on non-dominated sorting and quantum particle swarm optimization is proposed, and the performance of the NSQPSO is evaluated through five classical benchmark functions.The quantum particle swarm optimization (QPSO) applies the quantum computing theory to particle swarm optimization, and thus has the advantages of both quantum computing theory and particle swarm optimization, so it has a faster convergence rate and a more accurate convergence value.Therefore, QPSO is used as the evolutionary method of the proposed NSQPSO.Also NSQPSO is used to solve cognitive radio spectrum allocation problem.The methods to complete spectrum allocation in previous literature only consider one objective, i.e.network utilization or faimess, but the proposed NSQPSO method, can consider both network utilization and fairness simultaneously through obtaining Pareto front solutions.Cognitive radio systems can select one solution from the Pareto front solutions according to the weight of network reward and faimess.If one weight is unit and the other is zero, then it becomes single objective optimization, so the proposed NSQPSO method has a much wider application range.The experimental research results show that the NSQPS can obtain the same non-dominated solutions as exhaustive search but takes much less time in small dimensions; while in large dimensions, where the problem cannot be solved by exhaustive search, the NSQPSO can still solve the problem, which proves the effectiveness of NSQPSO.