In order to solve the problem of the multi-objective spectrum allocation on the joint optimization of maximal network utility and fairness of users in cognitive radio network, based on quantum bee colony theory and membrane computing, a novel multi-objective discrete combinatorial optimization algorithm, named membrane-inspired quantum bee optimization, is proposed. The global optimal solution of single objective can be searched in the elementary membranes, and Pareto front solutions which take account of network utility and fairness, can be obtained from skin membrane with the proposed method. The multi-objective optimization algorithm, which can solve both single objective and multi-objective optimization problems at the same time, is designed by the communication rules between membranes, the cooperative evolution of foraging behavior based on quantum state, and non-dominated sorting. Compared with classical color-sensitive graph coloring algorithm, genetic algorithm, quantum genetic algorithm, and particle swarm optimization under different objective functions, the proposed spectrum allocation method can search the global optimal solution of single objective as shown by the simulation results, and it is superior to classical spectrum allocation algorithms and existing intelligence spectrum allocation methods. The optimal Pareto front solutions of multi-objective spectrum allocation are also obtained.