To solve the problem that the optimization results of response surface method in multiresponse problem are affected by the model accuracy, a robust multiresponse optimization method was proposed to improve the grey TOPSIS model by taking the 3-DOF flexible parallel fretting platform of cell injection as the research object.Principal component analysis was used to solve the problem of multiresponse correlation constraints. The grey relational analysis and TOPSIS method were introduced to establish an improved grey TOPSIS model, and the grey relative closeness degree was taken as the comprehensive measurement index to transform the multiresponse problem into a single response problem. Finally, the main effect analysis of grey relative closeness degree was carried out to obtain the optimal design level of the parameters. The effectiveness of the method is verified by a practical case.