Abstract: In view of the problems of low efficiency of multi-stage liquid ring compressor and the immaturity of the design theory for inter-stage blade differences, in this study, the blade wrap angle, blade inlet angle, and blade outlet angle of the two-stage impeller in the liquid ring compressor were selected as the control parameters. The blade shape was parameterized by the fourth-order Bezier curve. Latin Hypercube Sampling was used to construct the initial sample space of the surrogate model, and the multi-objective optimization analysis was carried out considering the liquid ring compressor suction capacity and efficiency as the optimization objectives. Multi objective optimization analysis of blade profiles were carried out based on radial basis function (RBF) surrogate model and NSGA-Ⅱ algorithm.The results show that the efficiency of the optimal efficiency design in the two-stage impeller coupled multi-objective optimization is improved by 5.859%, and the suction capacity of the optimal suction capacity design is increased by 0.0107 m³/s. For the two stage liquid ring compressor, the optimal efficiency design has the same blade shape characteristics , with a small wrap angle, large inlet angle, and large outlet angle. The first and second stage impellers of the optimal suction capacity design have different blade shape characteristics, and the wrap angle of the second stage blade is larger than that of the first stage. The suction capacity of the optimal suction capacity design and the optimal efficiency design has a significant improvement compared with the original design, and the vorticity in the blade trailing edge is reduced. Reducing the difference in the compression ratio of the two stage impeller is beneficial to improve the performance of the liquid ring compressor.