Aiming at multi-objective military resources distribution with fuzzy time window, fuzzy cost and fuzzy risk, this paper builds a multiobjective routing optimization model with fuzzy constraints using the fuzzy expectation theory. A multi-objective quantum genetic algorithm is proposed to solve the model. The algorithm uses quantum bit encoding, and has been improved by introducing nondominated sorting and elitism strategy which avoid local optimization. The simulation experiment results show that the proposed model is reasonable and effective, and it has certain practical value in military resources distribution. Compared with the traditional multiobjective genetic algorithm, the proposed algorithm has a faster convergence rate to solve the above problem.