Based on the knowledge of fuzzy mathematics, microeconomics and swarm intelligence, this paper proposes a flexible QoS unicast routing scheme with the QoS(Quality of Service) satisfaction degree and utility. By using QGA(Quantum Genetic Algorithm), the scheme searches for a QoS unicast path which maximizes the network provider utility and the user utility while trying to strike a right balance between the two. Simulation results show that the proposed scheme is both feasible and effective.