Coupled optimization methods based on multi-objective genetic algorithms and approximation models are widely used in engineering optimizations. In the present paper, a similar framework is proposed for the aerodynamic optimization of turbomachinery by coupling the well known multi-objective genetic algorithm NSGA-II and back propagation neural network. The verification results of mathematical problems show that the coupled method with the origin NSGA-II cannot get the real Pareto front due to the prediction error of BPNN. A modified crowding distance is proposed in cooperation with a coarse-to-fine approaching strategy based on the iterations between NSGA-II and BPNN. The results of mathematical model problems show the effect of these improving strategies. An industrial application case is implemented on a transonic axial compressor. The optimization objectives are to maximize efficiencies of two working points and to minimize the variation of the choked mass flow. CFD simulation is employed to provide the performance evaluation of initial training samples for BPNN. The optimized results are compared with optimization results of a single objective optimization based on weighting function. The comparison shows that the present framework can provide not only better solutions than the single objective optimization, but also various alternative solutions. The increase of computational costs is acceptable especially when approximation models are used.